Sounds like a mad idea to me. Doom was hard enough on a full screen back in the day. On a tiny tiny screen like what is on that printer it would almost be impossible. At first I thought the OP was taking the p**. He/she could still be. BUT I did find this:- Canon printer hacked to run Doom video game - BBC News As I say tis a mad idea and that web page doesn't tell you how to do it but it does tell you that it was done if you believe the BBC. Other than that OP, Google is your friend, sometimes.
From the look of the article, this was a four month long project to exploit a security issue by a security researcher and was a lot harder than he initially thought! Unless you're comfortable with ARM assembly, electronics and have a lot of experience hacking devices already, you're realistically out of luck.
Of course, the article is also two years old and exploits a security hole that Canon said they'd provide a fix for quickly... no idea whether they did or not, but it makes the possibility of it less likely.
Also he just got the splash page working and didn't pursue getting the game to load and run. If you're wanting to get in to programing small devices I recommend getting an Adruino DUE R3. People are always pursuing porting games over to them. And for 25 bucks you can't go wrong.