The idea that the US protects Taiwan from a possible Chinese invasion over chips is one of those things that sounds believable but really isn't going to happen. From China’s perspective, the cost of war is much higher than the cost of developing these chips themselves. In the worst-case scenario, they would be 2-3 years behind the cutting edge, which is not mission-critical. Most electronics (civilian or military) do…
There are more reasons than chips.
First is Chinese nationalism. The Island of Taiwan has been under the control of various Chinese regimes over the centuries. Taking Taiwan is a rejection of the West and can be tied by to the "century of humiliation".
America has military posts in Korea, Japan, Phillipines blockading China's entrance to the larger Pacific Ocean. Having Taiwan would allow them to break this up.
On Taiwan is also a trove of Chinese art and antiques.