Can I still play the games if I have limb differences, or one side works better than the other?

Yes!

When selecting the task, use the parameter picker to choose the side of the body that you would like to use. (Maybe you want to use your strong side, or maybe you'd like to strengthen your weak side - you get to choose!)

Many of the app tasks have right/left/both as an option to choose. If they don't have that option, you can still try it - it may be that the game will work even if you can't physically use both sides equally.