I guess this kind of proves the whole point.
Without the AoE types written, people may forget or misunderstand what they are.

It's not the biggest deal. I get these are all circles but there are other circle AoEs that specify that they are as such.
Also not specifying whether the AoE is around the player or the target, while you can technically determine that from the range and radius of the skill, it should be written.

On the subject of it being a localisation issue, is this a factor in the Japanese text?