I played through the full demo (three battles) in one sitting (30ish minutes). I liked the tactical aspect (which reminded me of Final Fantasy Tactics and friends), not so much the map overworld part -- the latter was more confusing (and the opposing force doesn't seem to do anything, which makes sense for a demo). The pixel art was very well-done, as were the effects (you didn't feel like it's lacking any animation).
Other than the learning curve (which is a bit steep) and the confusing infantry-beats-cavalry (which is explained in the comments), I really liked the tactical aspect; you really have to think how to deploy carefully (eg. cavalry can charge anywhere but can get overwhelmed quickly; archers can hang back and snipe; cavalry archers are confusing; infantry swarm cavalry).
Most importantly to me, the game was straight-forward to play through: there's a convenient "next unit" button, and it auto-cycles through units with simple options like move (which you can use multiple times for far-moving units) and attack; ranges (including attack range when you move) are clearly indicated with red/green squares on the grid; unmovable tiles (eg. houses) look good and are easy to navigate around.
I liked the trigger system a lot (and used it in my games). The only criticism I would say is that missing the trigger entirely should probably be less of a fail; taking a page from Super Mario RPG, a successful hit should be skillfully double-damage etc. while a miss should be just a regular attack. As a game designer, I would say the design of the battles is pretty standard, nothing special or new other than the trigger system.
On the other hand, the overworld part is confusing; it's not really explained that you have bases, you can generate units/gold, and command units to move. I eventually generated three more units and tried to marge them, but clicked X and one just seemed to disappear. Not sure exactly how this works. Also, opponents didn't seem to increase in units or gold over time.
The characters were pretty well-developed also (in how they develop over time) and the overall picture of the game world is easy to understand. There were a couple of confusing sentences, but nothing untoward.
Also: please add a settings screen with options to turn off music!