Bearing on bike issues?

Father in law brought over his bike to have breaks adjusted and possible replace the tubes as they may have holes and the rear wheel looks wrong. It’s moving back and forth and I’ve never noticed before so wanted someone else’s opinion if this was normal. The rim doesn’t appear to be bent.

Looks ok. The plastic guard in there is what is moving around. Best way to check is to see if the breaks rub the tire at all when it spins.

Rim is fine, just compared to my daughters and it’s doing same thing. So appears to be normal.