There are certain games that Twitch won't be allowing streamers to play while on their platform but, it's not generally gamblers that will be out of Twitch.
That's why for streamers, they'll only have to pick another game where they can still stream without compromising and violating Twitch's rules about gambling.
As for Drake, he's got the platform and he'll be big wherever he goes, his audience and followers will go to just to watch him.
I don't think switching games will be all it needs. The streamer needs to find a sports betting-centric casino or a poker-centric casino based on the announcement, which doesn't tick most casinos since almost all of them have a variety of dice and slot games that Twitch has banned (yes, as long as any casino contains these games, they're not allowed to stream it).
So, we'll be making a policy update on October 18th to prohibit streaming of gambling sites that include slots, roulette, or dice games that aren't licensed ...
As you said though, Drake just needs to switch platforms but honestly, a loss in the audience is inevitable with that imo.