I don't think the Chinese give a rat ass how the foreigners think about China winning gold medals. That is not for bragging as suggested. The important information the Chinese people is to find out if they put their minds to it can the Chinese people compete at an international level, or even outperform the others! That is what the Olympic is all about to the Chinese. It is like the US shut down the GPS to China. Can China invent a different system call Beidou that performs better than the GPS?
It is not about gold medals, it is about a nation's people pursuing the sprite of being better for things they do. It is a cultural thing that most of western people won't understand. They may question why you Chinese put so much efforts to pursuing things that seem not worthy.
I feel that too when I was in Japan. I know a bit Japanese so they think I was one of them and being polite, but once they found out your Japanese is kind of foreignish, their face changes.
