I can’t speak to what specific information Twitch uses to process ownership requests, but the more info Twitch has to go on to ensure the legitimate owner of a game is the one making the request the easier it will be for them.
If the email address of a company attempting to claim ownership of a game matches the support email addresses for the game, and/or has registrant information that matches the company that is listed as the developers of that game, then that will make things a lot easier to prove ownership even if that domain isn’t hosting a website. If on the other hand it’s a gmail address, well then that’s more difficult to prove the person claiming ownship is the real developer and not a random person trying to maliciously gain access.