Is it possible that a radically different but equally effective playstyle exists? There seems to be an established "chess canon", whereby general principles exist for long term strategy in the game. There is a well-characterized set of openings, a small subset of which are even played, and even in middle to endgame one can identify named structures, attacking/defending pieces, point values, etc. High level players and chess engines will occasionally break "the rules" - but on a move-to-move basis, not consistently throughout an entire game. In others words, it seems like even though chess has room for a lot of creativity, that creativity lies within a well-established theory of what one might consider "basic technique". 

I am thinking of a project involving training an AI to play chess, but with a loss function that discourages common moves for that position - i.e. a chess engine that performs incredibly well but as unlike a human as possible. But before I launch into training, I'm wondering if such a thing is even possible. Chess theory is great for  teaching humans how to play, but is it possible that it is the only way to play chess at the level that top humans do? Are there any obstacles to the possibility of a completely different playstyle that would consistently break every rule in the book but still beat top players? Or does modern positional analysis rigorously rule out other strategies?

I'm a total amateur at chess, just a machine learning engineer with  an interest in the game - so I apologize if this question is trivial.
It's definitely possible there are strategies we don't know about. However, training your engine to specifically play contrary to all we know isn't the way to get there. For example, what would you do if one of your pieces were threatened? Our current knowledge says to not give it up for no reason, so would your AI therefore decide to give it up (because it's technically mathematically possible there could be some hidden idea 30-40 moves down the road?). You'd do better with random moves.

A better way to unlock hidden strategies is through a more bottom up approach. For example, AlphaZero learned on its own (without human knowledge), just using the rules of the game to guide it. From this, we saw a new style of playing that was basically unknown. But trying to get this new style of playing wasn't the primary goal.

Basically, it's fine to disregard human knowledge, but it's not fine to actively train an AI to play opposite to this knowledge. Here you're just trading one well established knowledge base for a vastly poorer one.