You are right to want to keep your chickens busy. Bored chickens end up with pecking and aggression issues. For chickens confined to a pen, I recommend keeping a compost pile in the run. It gives them a place to dig and scratch, with new things to eat daily. I have photos of my set-up here:
http://hencam.com/faq/compost-in-the-chicken-run/
Chickens don't need to "play" but they do need new things to investigate, dirt to dig in, and a variety of food.
I personally think that chickens in the house are a bad idea. They can't be potty trained, and wearing a diaper, which keeps the poop near the butt, is not a healthy thing for birds. They also need to be able to preen back there, which they can't do when wearing a diaper. Also, chickens shed copious amounts of dander, and they potentially care bacteria, like staph and salmonella. Once in a while it's funny to see them wander in the house, but it's not something to be done regularly (I know there are house chicken proponents out there. We can agree to disagree.) If you do insist on keeping chickens indoors, make sure that they get plenty of outside time so that they can dust bathe, scratch in the ground (essential for feet and mental health) and forage for greens.