@OP - I would say it's also fundamentally a roguelike as well as a puzzle game. The gods are probably the single thing that's most roguelike about it, rewarding learning, game experience and trying things out in often extremely complicated (but at the same time, entirely organic) combinations.
Personally, I've never looked up the list of things JJ punishes or gives out mana for. I basically am aware from experience of using him - teleporting, finding monsters, killing monsters, using buff glyphs and converting stuff is good. Getting him early is better. I know there's a risk of curse, mana burn and poison and that it's pretty rare to get any of those twice. There's a bigger risk of weakening, corrosion and such. Despite not ever looking that up I can actually use JJ very effectively in practice just from having the experience of using him.
For me the real elegance comes from the lack of redundant systems. Every single one of the gods plays out radically different to the others and is completely transformed by interactions with items, specific classes, bosses, other gods, dungeon layout etc etc etc... there are items I like more and less but none which are completely redundant (aside from subdungeon trinkets perhaps, but I think those are there more to lend a little flavour to specific runs and help flesh out the game's lore)... and I think the whole kingdom, puzzle and unlock system is a really good way of gating learning about those specific and individual features to a manageable level, while offering a mounting level of challenge.
I mean, agree to disagree, but I've always enjoyed the game as being more of a roguelike where your level of experience and depth of knowledge is as important as playing optimally and the mathematical dimension. Edit: Lujo has said something similar to what I said independently :p