The small trees were part of the beta phase of the battle system which originally intended to have more squares to allow a more tactical approach. I will change them if feedback is too negative about them.
As for the icons, I've been slowly learning pixel art to try and make icons and characters be of the correct size instead of having a script stretch them, but so far I've been unable to successfully learn how to make good pixel art.
And as for the moving function since the enemies don't seem to move in the video at all because the battles were restarted too often which makes it seem unnecessary, but it work by making the battle system both tactical and a quick frontal battle system.
How it works it's very simple, depending from your distance away or towards the target the character attributes are enhanced. The closer you are to your opponent the harder you hit him, but in return he can hit you very hard too. And the farther you from your opponent the more likely attacks will miss or hit for less damage, Also being in the same line as your opponent increases the chance of critical hits.
You can also protect other characters by placing yourself in front of them to lower the damage they receive and also raise the enmity(hate) towards the character defending which makes it more likely for an enemy to keep attacking that character instead of the weaker ones.
The above is the same for enemies as they can move and protect each other.
There are many other factors involved in the movement during battle such as stamina, weather, fields, field hazards(traps), etc. These factors add some depths to battles, but are not completely mandatory to use since there is no need to move next to the opponent to attack, making the battle work both as a normal turn battle system and adding some tactical aspects for people who want some more complexity during battle. And of course using the tactical aspect will make battles far more easier and interesting than standing in the same spot attacking through the whole game.