Wow! I'm surprised you had enough time to make an entire turn-based fighting system like this! I am definitely looking forward to what this will turn into :)

The fact that you could really easily just have a battle going on quite quickly after opening unity is great! I had to look at the docs to find the Tools/Demon Cube popup, but after that, it was smooth sailing (little confusing that there isn't a demo scene though). 
I think you could have gone the extra step and built a demo for like WebGL, so that people without unity can still take a look at the wonderful tool you've made :0

Code is a little intimidating to dive into, D:  I think readability could have greatly improved by splitting the scripts into more manageable chunks, (I'm looking at you, UnitActionsDatabase.SpecialAction()) and I feel like some objects could have used a little more documentation or cleaning up. 

I also like the circle showing whose turn it is and the slap action :)