Taiwan is winning that way. Nvidia may design the chips in the US, in the same way that ARM does out of Cambridge, but they're manufactured in Taiwan.
The "stealth" war is over Taiwan and if China succeed in taking complete control of it, it's game over for Nvidia. China doesn't exactly care much for IP rights.
TSMC build the chips yes, but they are built at TSMC with the worlds most advanced semi conductor machines, of which there is only one company on the planet capable of building such complex machines. They are built by Dutch firm (with very strong American interests) ASML. Which run on, you guessed it, American built software. Taiwan are only winning the war because they are under the wing of America, so it is essentially America who are winning the war, it's their chips, their designs, their machines and their software. They are just using Taiwan as the location to build them, but not for long as TSMC is coming to America, plants are being built now. It is impossible for anyone to say it is Taiwan winning that way when their fabrication plants run on what is basically Western / American owned and designed machines and American software. Without America they would not be winning anything. America have allowed them access to ASML and the software needed to run their machines. If China took Taiwan, they will no longer get access to the latest ASML machines or software, meaning China's chip progression would once again be frozen in time. As global fabrication processes move forward as they have for decades led by ASML technology. It certainly would not be game over for Nvidia if Taiwan was taken. America have the advance chip designs from Nvidia, they have the advance machines, they also have the vast engineering knowledge and software. all they will need is a place to build them. Which with TSMC opening in Arizona and other US locations means that wont be an issue. China on the other hand are the opposite, they have non of that. They have places to build the chips, non of the other attributes that make up the eco system that allow the USA to build such complex chips.
In short it is very difficult for anyone else to do it, apart from TSMC, thanks to Americas influence. America are rushing to build semi conductor plants in American right now. America also have the full eco system which as of now no other country has. Something crucial in building advance microchips.
China do not have access to the ASML machines, software, or the tight engineering back and forth that is needed between chip designers at say Nvidia and chip fabs such as TSML.
AMD somehow got a form of their first generation Ryzen processor design approved by congress to be given to China, for them to manufacture. They were handed the blue prints on a plate about 7 years ago now. China manufactured the same chips as AMD, using their own machines, fabs and knowledge, the chips turned out to consume about 3x as much power as their American counterparts and have nearly half the processing capability. These are the same chips, built from the same design. It just shows how valuable the machines, software and decades and decades of knowledge are to building these extremely complex pieces of silicone. Something America keep very close to their chest.
It is no secret microchips will win a war, it is also no secret that America are by far winning that race, you just need to look at any of the huge tech company's which are all almost American, to see why. Your nuclear powered submarine that is capable of locking onto 30 targets at once does not run on magic, it runs on silicone. Extremely fast and precise silicone, that no one else apart from the USA has the complete eco system to design and build them. If China took over Taiwan on it's own, they would have some machines, some outdated software all from the manufacturing aspect, you wouldn't have the design experience, skill and knowledge from say Nvidia, Apple or AMD, or the very latest in cutting edge ASML machines. Extremely advance chip design relies on tight integration of all aspects of the design and manufacture process, if you miss a piece of that puzzle, you are not making advanced chips. China taking Taiwan will give them some pieces of the puzzle but not all, so as we saw when they were allowed to build AMD chips, they won't be any good.
With AI again now being led hugely by once again, American company's, the gap will grow wider, as AI will improve every aspect of the design and manufacturing process.
ARM is also very different to say NVIDIA, ARM licence the designs to ANYONE, even China. All the Chinese based designs are pretty slow though. Apple and Nvidia based ARM designs? Blisteringly fast. Why? Because of the design integration. The design of NVIDIAs chips are totally different in the sense that they do not sell the designs, not yet anyway, but even when they do, the actual design will be a closely guarded secret. They certainly wont give company's an open book into their chip designs as ARM does, thus it is like comparing Apples to Oranges.