The author clearly means Nvidia losing face with respect to China.
This concept of "losing face" may seem like just a small word or minor loss of reputation to Westerners, but in a sense is more important in China (and to varying extent all over the Far East) than even money.
If the story is true, and the depth of detail leads me to believe it is very likely, then the reputational damage to Nvidia would be high and, more importantly, entrenched (an aspect of face that makes it different from mere temporary reputational loss) due the public service, government angle and the size of the proposal.
That has nothing to do with it. Why would China even meet with Nvidia if their CEO being Taiwanese was an issue? There are tons of Taiwanese companies manufacturing in China and China has interests in Taiwan as well.
Assuming that this story is true (since it's based off "Rumors out of Beijing").
I'm just speculating. I'm not making a stament of fact. However, it's not out of the question that CN cares about the politics of the people who deal with CN.
The connection they imply is doubtful. They give no date for the Nvidia negotiation, but (assuming it isn't misrepresented) it must have taken a lot of time (enough that the Chinese could pick something from AMD in the end). And I doubt Linus heard about it, either (the “behind the curtain reason for Linus' frustration” idea must have come from someone unfamiliar with him or the video of the event). The only commonality is that both find Nvidia hard to work with, in different contexts.
My interpretation is that Nvidia caused the Chinese to lose face, and this what will doom them to lose future contracts. I've been living here in China for 6 months now, and the social aspects of business, like face, are really nuanced, but so so important. I don't really understand them yet.