Q:

"win by getting a head"

I suppose that the picture above is some kind of a joke. But I am not able to catch the point. I would understand if there was something like "where the winning means that the head will stay on your neck". Or is "get a head" an idiom?

A:

To get ahead means to make progress, to get ahead of someone means to outrun or outpace them, to leave them behind.
Of course, with a guillotine, one person (the one operating the device) gets a head and another loses a head. 
Maybe in this game the goal is to decapitate your opponents?
There's another bit of wordplay with "revolutionary".

