Hope that there's a modded version that doesn't need play services. They exist for a fairly decent range of games. The less the game relies on an external server, the better the chance it's out there.

For stuff that doesn't have any need to check for play services, or verify anything, you can just copy off the apk file and do what you like with those.

Data is harder. Most games rely on Google backup. The ones that don't, you may not be able to access to back up yourself. I dunno what the current options are, but it used to be that titanium backup on a rooted device could make a full backup to install on a different device. There was one that didn't require root, I think it was called helium? But I never used it.