I'd agree that it's an awesome game, but I wouldn't agree that it's a puzzle game. I'd call it action-puzzle, the same category as stuff like Lolo, Boxxle, the Klonoa GBA games, Lode Runner, Lost Vikings, etc. I guess it's kinda nitpicky, but I really do think a distinction should be made, since such games are drastically different from the ones commonly considered "puzzle games."
If we're talking action-puzzle though, I totally agree with you. Solomon's Key kicks ass. Did you know the arcade version made it onto a Japan-only Tecmo classics compilation for PS2?