The Game Center app was removed from iOS with the introduction of iOS 10 in September, 2016. Since that time, each individual game communicates to Game Center.
Since you have more than one game crashing, the highly likely cause is you have filled your iPhone Storage. Assuming you have a current iOS version, check Settings > General > iPhone Storage and be certain you never have less (hopefully much more) than 10% of the iPhone's total storage free.