Nope. It does come with a "game key" which seems to be a string of randomly generated words (distinctly not a Steam key), but I have no idea what its intended function is.
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So I finally got through what I can only assume is pretty much the entirety of Domino Dungeon, I have the red key, and suddenly the ceiling-mounted platforms that lead to the red door have vanished and I can't continue.
Is there somewhere to submit this? I can't believe how much time I just wasted on that level for it to bug out on me.