Yeah, I think the fights are pretty easy once player gains few levels. I even cut base Strength in half before releasing and it still wasn't enough.
The element that's supposed to make them harder are Trials. You get a randomly generated task at the start of battle, like "don't take any damage", which will award bonus exp (and more in the future) at the end of the fight. You can view the details of them by holding Tab, and since last version you can also hover over the icon (on the webm you linked it's the heart). So basically you could just ignore them, or you could try a bit harder to complete them in order to cut down grinding time.
For next demo I'll try to get more variety on top of this by adding Slash/Pierce/Crush damage and defense, as well as more skills for each class to encourage more strategy in fights.