Not a game really, but still something to keep the guests busy. Put white onesies of different sizes at each table along with fabric markers. Have everyone decorate, draw a picture or write their favorite quotes on the onesies. That way baby has a bunch of onesies to grow into and mom has cute mementos from her shower.

Baby jeopardy was a big hit at mines!

Pinterest girl that’s all I got

Tissue game , put baby food in diapers guess the flavor

We did an emoji game that was guess the baby book and a what's in your purse. It's a list of random items and you get so many points for said item. I liked these because you dont have to get too involved lol. Whoever had the highest score/correct book names got a gift basket/prize. Pinterest has a ton of good ideas!