Is there a way to transfer an iPad 2 to a different user without losing the game scores? I just bought a new iPad and would like to give the older iPad 2 to my kid. He's used the iPad a lot to play a variety of games, all under my user account. Is there a way to create a new user account for my kid (I'll make it part of Family Sharing, etc) without losing the game scores?
The saved games are usually stored locally on the device, even if they are synchronised by iCloud. If you sign out of your iTunes account and sign in with his new one, there shouldn't be any loss of save game data at all.

If, however, you want to wipe the iPad and set it up anew for him, you'll need to backup the save information and restore it to the iPad after the clean install. To do this, I would recommend iMazing (formerly Disk Aid). It's a great app, available for both OS X and Windows, that lets you drill down into your apps to retrieve data.

I would recommend doing a full backup in iTunes first, then use iMazing and save the "Documents" and "Library" folders from each app with a save game, so you have two backups just in case anything goes wrong. Then, once you've restored the iPad to factory settings and reinstalled the games, just use iMazing again to copy the folders back in to their respective apps.