I think it falls more under action. There's a little bit of strategy to the upgrades, but it's mainly just trying to juggle killing the different attackers. It's not the most demanding twitch gameplay, but it's still twitch gameplay.
I'm not trying to spam a post a moderator doesn't think belongs here, but I just wanted to say that I had the same thought when I played. It struck me as much more of an action game than a strategy game.