Industrial and commodity multinationals face the most pressing concerns, as they scramble to stem the profit slide from weaker consumption. Caterpillar cut back factory production, with industry sales of construction equipment in China dropping by half in the first six months of the year.
Smartphone makers, automobile manufacturers and retailers wonder about the staying power of Chinese buyers, even if it is not shaking their bottom line at this point. General Motors and Ford factories have been shipping fewer cars to Chinese dealerships this summer.
It is not just companies reassessing their assumptions. Russia had been turning to China to fill the financial gap left by low oil prices and Western sanctions. Venezuela, Nigeria and Ukraine have been heavily dependent on investments and low-cost loans from China.
More from the New York Times:
China's big spenders pull back, as stock market shudders
China turned to risky devaluation as export machine stalled
As markets flail, China investigates large brokerage films
The pain has been particularly acute for Brazil. The country is already faltering, as weaker Chinese imports of minerals and soybeans have jolted all of Latin America. The uncertainty over China could limit the maneuvering room for officials to address the sluggish Brazilian economy at a time when resentment is festering over proposed austerity measures.
The weakness in China is even compelling officials at the United States Federal Reserve to think more globally, as they consider raising interest rates. William C. Dudley, the president of the New York Fed, said on Wednesday that a September rate increase looked less likely than it did a few weeks ago.
"The entire world is focusing now on China, watching this crisis unfold," Armando Monteiro Neto, Brazil's minister of development and foreign trade, told reporters on Tuesday in Brasília. "Brazil is already feeling the effects of China's deceleration. If the situation gets worse, the impact will get bigger."
The trouble is, the true strength of the Chinese economy — and the policies the leadership will adopt to address any weaknesses — is becoming more difficult to discern.
China's growth, which the government puts at 7 percent a year, is widely questioned. Large parts of the Chinese service sector, like restaurants and health care, continue to grow, supporting the broader economy. But the signs in industrial sectors, in which other countries and foreign companies have the greatest stake through trade, paint a bleaker picture.
Adding to the worries are recent events like the deadly explosion of a hazardous chemicals warehouse in Tianjin, which has delayed shipments through one of China's biggest ports. Labor protests, already rising, jumped sharply across coastal China last week over unpaid wages at struggling export factories.
The leadership, concerned with maintaining social stability, has been quick to act, making aggressive moves to prop up the stock market, inject money into the financial system, and generally stimulate the economy. But President Xi Jinping doesn't have much experience managing a downturn, and some economists worry that the government is making knee-jerk decisions that will do more harm than good.
Many company executives and global economists say that forecasting China's growth has become so hard that they are hedging their bets for the time being. "This is a complete black art right now," said Tim Huxley, the chief executive of Wah Kwong Maritime Transport Holdings, a large Hong Kong shipping company. "I can't make any long-term decisions based on what is happening today, and so I just keep our fleet running until we get a bit of direction."
The problems have been building for months in areas like commodities and industrials where just modestly slowing growth in China has been having outsize effects.
For more than a decade, prices surged for iron ore, a main ingredient in making steel, as new skyscrapers, rail lines and other infrastructure were built across China. Last year, BHP Billiton shipped enough iron ore each day to China to fill the Empire State Building.
Now, the industry is retrenching in the face of China's weaker prospects and diving commodity prices.
Read MoreChina's 'QT' is the real global economic threat
Vale, the Brazilian mining giant, is racing to unload assets. In Australia, Vale and its Japanese partner, the Sumitomo, sold a coal mine in July for just $1, after it had been valued at more than $600 million three years ago. In Argentina, Vale is trying to sell a potash mine in which it invested more than $2 billion.
The fallout in commodities has been especially painful for emerging markets that depend on sales of those resources.
With Brazil's revenues declining sharply this year, President Dilma Rousseff's government is coming under criticism over the country's dependence on China, which surpassed the United States as the top trading partner in 2009. Brazil's exports to China fell 23.6 percent, to $24.7 billion, in the first seven months of the year from the same period in 2014.
In an editorial on Tuesday, the newspaper O Estado de S. Paulo described Brazil's relationship with China as "semi-colonial," claiming that the country's economy "depends in excess on Chinese prosperity."
Ilan Goldfajn, chief economist at Itaú Unibanco, one of Brazil's largest banks, said he was already forecasting the economy to contract about 2.3 percent this year, without factoring in the possibility of a hard landing in China. "China is the most important risk factor for Brazil," Mr. Goldfajn said.
China was supposed to be the financial savior for Russia.
Last year, Russia signed a $400 billion natural gas deal with China. China would help finance a nearly 2,500-mile pipeline to ship fuel from Siberia. Russia trumpeted that it would eventually sell more natural gas to China than Germany, now its biggest customer.
But the prices that China is willing to pay for the gas are dropping so low that it may no longer be worthwhile to build a pipeline. The Russian energy giant Gazprom has cut its planned capital outlays this year for the first leg of the pipeline by half, Dozhd television reported.
"China is an unclear country for us, opaque," said Aleksandr Abramov, a professor of finance at the Higher School of Economics in Moscow. "We don't know what to expect," he said, adding, "Clearly, the situation will worsen in Russia."
Some of the latest pressures reflect a belated recognition by businesses and politicians that China had been slowing down.
Automobile manufacturers cut their shipments of new cars to dealers by 7 percent in July, compared with a year earlier. Retail sales had not suddenly tanked, said Cui Dongshu, the secretary-general of China's Passenger Car Association, which represents manufacturers.
Rather, too many cars had been sent to dealers' lots in previous months, he said. In other words, manufacturers were slow to see the economy's deceleration and waited too long to throttle back their factories.
"What manufacturers are doing is adjusting inventory levels to the 'new normal,' " said Bill Russo, a former chief executive of Chrysler China, using a favorite phrase of President Xi Jinping of China in recent months to describe an economy that is expanding at a slower pace.
Similar adjustments are taking place around the globe.
For years, Germany has been well positioned to profit from Chinese growth because it specializes in machine tools and other factory equipment. Most important, China acted as a counterweight to the chronically slow-growing markets in Europe.
Now, major German exporters are seeing signs of pressure.
Trumpf says that sales of its signature product, machines that automakers use to cut sheet metal that sell for about 500,000 euros ($566,000) each, have continued to grow in China. But in May and June, sales of less-expensive cutting machines flattened and began to decline. At the bottom of Trumpf's product line, sales have fallen sharply since November for machines often purchased by start-up companies.
How industries and economies ultimately fare will depend on how long the slowdown and how deep the economic woes.
Read MoreGoldman: Don't freak out about a global recession
Demand remains strong at Boeing for its 777-300ER and 787 jets, models that are capable of flights lasting 10 hours or longer, to Europe or North America. Long-haul international travel from mainland China soared nearly 30 percent in the first half of this year compared with the same period last year, Randy Tinseth, the vice president for marketing at Boeing's commercial aircraft division, said during a visit to Beijing on Tuesday.
So far, it has been mixed for technology players. Timothy D. Cook, the Apple chief executive, said on Monday that business had stayed strong in China in July and August. But Meg Whitman, the chief executive of Hewlett-Packard, said in an earnings call last week that China's consumer market for printers and computers was "pretty soft," although demand from businesses was holding up better.
In the end, much of the China story will come down to whether the expectations meet the reality. Andrew Mackenzie, the chief executive of BHP, captured a broader corporate view on Tuesday when he spoke glowingly about China's potential in the decade to come and predicted continued profitability. But he conceded that the country's steel production would most likely "grow a little more slowly," citing a forecast that works out to just 1.4 percent annually — a figure that sounds more like Europe than the formerly go-go economy of China.
A similar realization is taking place in various corners. "We had five fabulous years in China, of course, where we grew strong double-digit, and it has been gradually slowing down," Frans van Houten, chief executive of Royal Philips, the Dutch conglomerate, said on July 27. "I think, going forward, we need to be much more modest on expectations with regard to China growth: That's just being realistic."