You can define Deadpool or Team Fortress 2 as comedy games, but the gameplay itself isn’t funny. The gameplay is fairly standard. The comedy is in the music, the text, and a bit in the art. But the gameplay is dry.
So is funny gameplay impossible? Not at all. It’s just that it isn’t a common practice to use it.
Have you ever played I Wanna Be the Guy?
(http://kayin.pyoko.org/iwbtg/)
I Wanna Be the Guy is a parody of old video games. It’s supposed to be unfair, but in a way that’s possible to master. The game is not only filled with obvious hazards, but also dozens of completely hidden traps. And you’re almost guaranteed to be hit with everything at least once. The game is meant to be lost thousands of times before finally beating it. And most every time you die, you laugh.
Why does losing this game warrant laughter? Because the basis of comedy is misdirection and timing.
It’s key that this game is not only hard, but harder than you’d expect. Every screen you enter, you wait a second and scan the visual hazards. This is the set-up. You think to yourself “I think I can make it." If you can make it past the first screens, you’ll be skillfully dodging obstacles for a set time. Then the game unleashes unfair trap #1. The punch-line is that you die.
Player evaluates level -> Tests skill -> Unexpected trap goes off at interesting moment -> Trap deals consequences
This is the basic structure for comedy in video games! If you follow it, you should be able to make jokes through many different types of gameplay.
Of course, this isn’t the only way to turn gameplay into a joke. But funny games are almost nonexistent, so it’s good to start somewhere.