1. Further suggestion (as those from Kurutte are valid too): the resolution of the rolls are displayed a bit fast; I would have let the player click to skip when he wants to.
2. Also, maybe it is a question of getting used to it, but I wonder whether it is rather difficult to think strategically about the pincer rule. I may be totally wrong on that count and not have fiddled enough with it, you want a second opinion. ;) Thinking about it, it may be workable, I managed to fare reasonably in some combat. :) Discard my remark altogether, I just let it as a ‘first thought’.
3. Did I misunderstand the pincer rule? I had both a 3 and a 2, and the enemy (the first one) had a 1, so I thought this would result in a 1-2-3 pincer, but it did not! Does that mean that the pincer cannot use the lowest (and highest) dice? Edit: ah, maybe a pincer has to involve the lonely die as the middle one?
4. I see the Escape key opens a nifty menu; is this menu predefined? (From PyGame I guess, seeing the extension .py for one of your files?)
5. The visuals for the enemy cubes/dice are funny, it sounds like Pokémon gone cubist. XD

I tend to rather strongly oppose the classic JRPG turn-based combat system as mindless, but I feel yours precisely injects some sense/reflection into it — which is highly ironic, since you added… randomness. XD

I can relate to your comment on how we may resolve to cut promising aspects of a game because of the Great Evil Deadline. Well, you can always remember that the game still lives on after and that you can enhance it. :) No worries, it is perfectly understandable when the presented game has shortcomings.

Is there a browser version?

I like the idea! However the pincer mechanic needs to be explained a bit more, maybe with an example in a tutorial just so it made more sense. There were times I took massive damage and I didn't know exactly why. Also some SFX would be nice. You'd be surprised how much it helps with game feel.