If you try to play the web version's mini-games, it will tell you your Pou is too tired to play them.

To get energy, you need to both:

• Feed Pou whatever you feel like it in the Kitchen to fill up your Hunger meter.
• Clean Pou (soap, shower, towel and toothbrush, in that order) in the Bathroom to fill up the Health meter.

Once both those meters are filled, you should be able to play the mini-games until they get to low values again (do the whole process again when that happens).