Are x move checkmates overrated? for example, 9 move checkmates.

Experience has taught me that the lower rated the player, the more important these things are.

4 move checkmates are not gimmicks. You won your game against Tin1555 with a 3 move checkmate, and your are only 607 in rapid. Much stronger players will be able to play 3 and 4 move tactics much more regularly. What you have wrong is that it is not about memorizing those moves. It is all about pattern recognition (and then calculating to see what combination of moves make the tactic work) which is what seeing tactics in games is regularly about. As far as 9 move checkmates even very strong chess players don't see them how you are probably thinking. It comes down to pattern recognition if they see that in a game. They may see one pattern for a tactic, and see that it leads to another one that results in checkmate. So they did not see all 9 moves usually. They just saw that one pattern leads to this other pattern. Not them just calculating every move for 9 moves, and playing them all correctly. Very strong chess players may be able to do that in endgames when there is not very many pieces left on the board, but even then they are probably using some sort of principle, or concept that tells them in what direction to look for the tactic.