Not quite the actual rules of chess, but that is an interesting variant. And you're right: under that rule, your position above is indeed mate. Perhaps we can call this the "very foolish king's mate"? ;-)

sorry the way i play with my friends is if your in check you can only move your king

oh well sorry for the confusion

This is not known as the Fool's Mate because 2...g6 blocks the check. That's also why White's second move is listed as 2.Qh5+ and not 2.Qh5#.

The Fool's Mate looks like this

This is also known as the fool's mate