aren't there games that forbid streaming them
And that's one of the problems of creeping copyright maximalism that will lead people to be fed up.
How do these licenses gatekeep streaming when the only right granted by copyright is control over who can copy?
Don't forget the justification for copyright in the US is "To promote the Progress of Science and useful Arts". I don't see how blocking streaming fits under that justification.
Yes, they always require special licenses. GTA 6 won't stream to PCs on day one for example.