Ability is easily the mos accurate description. What the hell does perk mean anyways, it means a benefit of something. I suppose it's a benefit but by that logic you may as well call weapons "perks"
It's an ability because it's a talent you have developed.
Perks are for Fallout, though they were misnamed there. Feats are for D&D 3rd(+) Edition and were similarly misnamed. "Ability" suits the subject matter much better, as it applies to having the ability to do something you may not have before.
A perk is a one-time benefit that comes along with something owed you; in this case it's a level. It's short for "perquisite." Ugly word. However, a perk isn't necessarily useful beyond its initial receipt. Most often it's just a neat-o burrito, mosquito one-off.
A feat is something you have finally accomplished, but it's over once you've done it - until you do it again. It's a noteworthy event. Do it often enough and it drops in status from a feat and is now an ability, since you are able to do it reliably. The only exception I could find was a reference to an obsolete definition that refers to a feat as synonymous with a particular skill or knack. Since abilities don't go away and you can do them any time you wish after acquiring them, the name fits.
In the modern world of HD, I certainly hope gamesas isn't considering saving UI space by going with a name because it has less characters.
I do agree that a passive statistic boost isn't an ability, so another name may be needed. I wouldn't mind descriptive sentences like, "Your hard work honing your abilities has paid off, as your XX is now increased!" or "Your hard work honing your abilities has paid off, as you are now able to YY."