How serious is the no checkmate with a pawn rule?

I’ve noticed several puzzles where it’s allowed in several where it’s not.
I’ve also won a game or two with a pawn checkmate.

Is it just a technical issue that the computer ignores it or is it only a relevant rule in serious games?

I'm not sure what happened in the games where you won, but the rule is that the checkmate can't be from a pawn drop. You can still checkmate with a pawn as long as it's not a drop.

In real life doing such a move will lead to an automatic defeat. That's gotta be the most painful way to lose a game, ha ha (happened to me once at 81dojo).

Yeah, pawn drop checkmate is simply not allowed at all. It's just one of the rules. I think you might have been mistaken.
To be clear if you don't know: a pawn MOVE checkmate is okay. Just not a pawn DROP specifically.

You can't post in the forums yet. Play some games!