Most games nowadays backup to the cloud. If you have some that don't, look into something like Helium.
https://play.google.com/store/apps/d...ikdutta.backup
It doesn't require root, but allows you to backup app data to transfer to another phone.
Regarding your LG G4, you're one of the lucky ones if you've gone this long without the infamous bootloop. I'd suggest going with something else and newer. If you get another G4, it'll be used or refurbished at this point, and could still suffer the bootloop. I personally went from the G4 to the V20 and couldn't be happier.