You see 3 types of rectangles in the video:
This is basically the player controller, which handles movement and collisions, like the one in the Platformer demo. It usually collides with the level, but not with the blue or green rectangles.
Represents the "Hitbox" of the corresponding player. It can for example register other overlapping
Area2D nodes, like the red rectangles.
Represents some kind of "source of damage", it is basically an
Area2D node, wich is registered from hitbox-areas. It could be a script attached to it, with stats for the dealed-damage. The Hitbox could get these stats, when the signal
area_entered is fired, with something like this:
var damage = area.get_damage()
print(owner.name + " takes " + str(damage) + " damage!")
Here, you need to know, how to use Signals.
simple Example scene:
AnimationPlayer, Sprites, AudioStreamPlayer, or whatever you need too
How it could work:
KinematicBody2D is just the player controller, like mentioned above. The player controller allows different input for different attack-animations. A simple punch-animation would just show up a DamageSource for a short period of time, so the other characters Hitbox could register a collision with it, so the character can take damage.
Here, you need to know, how to use Animations.
Also I suggest you to have a look at the Phyics introduction.
Good luck! :-)