A friend threw a baby shower for me, I remember there were one or two quick and easy games - she supplied a few little gifts as prizes and none were handed over (or expected to be) to me. Another shower I attended had some cute games including the tray one - I think we got bonus points if we could also write what the MTB was wearing, but the tray of items was definitely the main part. I won one game and tied another, and there was no apparent pressure on any game-winners to give the prizes to the MTB.
So count me as another who would not only not expect to hand any prize back to the MTB, but would be really put off if the host or others "encouraged" that.
On the games front, I do like the concept of having a few simple games planned, particularly if the attendees come from several different social circles, because they can work as an ice-breaker. However, if the party is moving along and people are already really animated, I would save them for lulls in the conversation (and be ready to skip altogether if time runs short).