Twitch Interactive is a subsidiary of Amazon, not Google, so Twitch should still exist. Whether Stadia takes off and Twitch has to adapt or go down due to the competition, remains to be seen.
Stadia will use the YouTube network of servers. Stadia will encompass both Steam type service (a way to buy games), and YouTube type service, where games can be uploaded (or now streamed directly).
I doubt any of the features of YouTube will be affected since even Google are still referring to the network of servers being used as YouTube. At most you might start seeing ads for Stadia subscriptions or trial periods on YouTube.
Think of it this way, if YouTube as it currently exists were to go down, that would mean all those servers would be converted to Stadia direct streaming servers, and there would be tons of lost content from those who have uploaded videos to YouTube. That would start Stadia off with a LOT of disgruntled YouTube users. It would also cause a lot of concern for the very expensive ad space of YouTube.
Putting that much stock into a completely and new relatively untested direct streaming service would no doubt make the service risky for those whom otherwise would trust the tried and true YouTube for ad space. Basically changes this big have to be handled carefully, and tearing down YouTube is NOT the way to do that.
My main skepticism regarding whether Stadia will be successful to the point of competing well with currently existing forms of buying and playing games, is they say they are going to port them to Linux first like Valve did with Steam Box.
Valve promised better performance with the Linux ported games, and they are experts at coding games. As it turned out most of their ported games had worse performance than the original Windows versions, with a few being equal.
Of course there were other reasons Steam Box pretty much flopped, but the games performing worse than on Windows was kinda the straw that broke the camel's back. The same could happen with Stadia.
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