I would say this game isn't an incremental game it's a puzzle game with incremental elements but it's missing what I consider to be a core element of incremental games which thinking more on it I come to the conclusion you can't have an incremental puzzle game it's either an incremental game with puzzle elements or a puzzle game with incremental elements because the core of the two genre's are mutually exclusive I consider a core feature of incremental games is that there isn't a strict sequence that has to be followed ... going from the definition you posited in your other review reply posts the castlevania and metroid games would be incremental games and no one considers them such
that said despite it not being what I'd consider an incremental game (despite it being inspired by 3 incremental games) it was fun until the battle I'm going to give the battle one more shot before I give up on it