I always liked the video game urinals... at least with those they take your pee no matter how well you are doing.

The problem with combining a household appliance with a video game is the fact that there aren't a lot of appliances that don't already play video games. Your phone? Yup. Tv? Yup. Computer? Yup. The ones that are left are either dangerous (disposal, microwave, stove) or impractical (fridge, ac, heat, ect).
About the only thing I can think of would be in a commercial application. A pop machine with a built in video game. If you do well enough, you get your change back. Maybe a nice game of ice-climber.

I think they already have those in japan though.