If you play in person and someone makes an illegal move - just take their king and immediately win

Happens all the time with people I play. They don't see that the move is illegal  (put themselves in check) and just carry on with their idea and I get to say "nuh-uh" or shake my finger and point to the checking figurine. 

I should just take the king and end the game right away, and I truly wonder why that is not a thing in chess.

And here is the thing about that: This one guy I was playing was not very good (I am not very good, but compared to me, a lot worse) and he kept doing this all the time. We played every day a couple of games. The first few days, I kept reminding him. Yesterday I started capturing his king and win the game right away. I have only done it twice and he has not done it since.

Of course, they have official rules there and don't allow it.