Trouble Transferring Games From Xbox 360 To Xbox Series S

If I were to download that game on Xbox 360 on the same xbox account, would the game transfer to series s?

Hi,

Since the Series S has no optical drive you'll need to by the digital version of MCC from the Xbox Store to play in on the Series S.

You can transfer the already installed game across consoles either via a network transfer or external storage device, but you'll still need to buy the game again to play on the Series S. Transferring, copying or moving the game is often quicker than downloading the game from the Xbox Store.

As long as you're signed into the account that purchased the games, they should be listed as ready to install in your library in Games and Apps. If they were purchased on a disc, you would need the games digitally in order to play them on the Series S.

Nope. For two reasons. The Series S won't recognize the games from an external drive and you need a license to play the games. Since they were purchased on disc, the disc has the license and would need to be in the disc drive to verify you own the game.
Since the Series S doesn't have a disc drive, the games have to be purchased digitally.

You would have to purchase them digitally if they're still available. You should be able to buy them through the console or xbox.com