That basically looks like pocket doors. There are a ton of DIY tutorials for installing them. You'd probably need them to be on some sort of a track so when one moves, the other moves too.
I've seen people online use a small motor from a retractable car antenna to make small doors (like to a chicken coop) close with a timer. You could probably replace the timer with a motion sensor.
The last step would be making it look like whatever game that is.