I'm not familiar with the circumstances around this, but I think some people are making assumptions about what is in this contract. From the quote above:
I can still record a bit on [another site] as of now, but eventually 100% of my recorded/streaming play will be on Chess.com.
In other words, his contract clearly does NOT forbid him from playing on other sites.
Equally obviously, Chess.com is not paying him to stream from other chess sites, so John is choosing to go with the site that IS paying him and giving him a "career-changing opportunity"; he says that he is
really excited to be a part of their push to professionalize chess (especially when it comes to streaming). I'll still be producing as much of the same content as ever, just on Chess.com
I would actually suggest that because Chess.com is paying him for stuff he was previously not being paid as much for, that he will be able to start producing even better content, attracting more people to the game and helping grow the overall market for Chess.
So is he allowed to stream from elsewhere?
They bought Ben Finegold as well ...
We*