Genocide is any attempt to destroy a group of people or their culture. Killing is one method of commiting genocide, but imprisoning members of a culture in an attempt to destroy that culture is also considered genocide.
Where did you find a definition about the culture? Searching genocide on google brings up only definitions including killing, and the word itself means killing people not culture.
No, genocide has a pretty precise definition, actually.
I'm sure I'll get downmodded to hell for pointing this out, but what's happening in xinjiang right now is a mass internment, with terrorism as the casus belli. It might turn into ethnic cleansing in the near future. It's unlikely to turn into genocide, and it's definitely not right now.