So, i'm wondering that if a creator put the game back on, will it be kept in the library or do i have to claim it again?
Games have unique IDs. It depends how the games were taken down. If they were mereley put into restricted mode, nothing changes. Actually, one should still see the games, if they were claimed. But no one else could.
If they were deleted, one cannot resinstate the games by simply chosing the same name and create the same url. That does not work. Also, there would not be any re-claiming possible. From what? You need a 100% sale with claiming enabled or a unique purchase page - which you do not have, since it is a new game id. And if you talk about claiming, that means, we are talking about a paid game. You can only claim games that you paid money for.
https://itch.io/t/3693485/do-not-update-your-games-by-deleting-them-and-uploadin...
And if that was a delete take down, you as a customer would not have to make that ticket. The developer that would ask for an undelete would have to do so. Maybe support can help.