Sure, I'd say it's an RPG as much as, say, Dragon Age: Origins was an RPG. You've got stats, you deal numerical amounts of damage that are visible on the screen, you've got a customizable character, and you can pause the game to think about your next action strategically, a luxury not afforded to other genres. Haven't played it in ages, but it struck me as an action-RPG when I rented it.
I think it very much is an RPG. I played it way back then and thought it was your typical action rpg. It gives a third person aspect gameplay although you can choose to play first person if you want. Since you only control one character, I suppose that makes it more of an action rpg than anything else either. I do tend to prefer open world rpgs, or turn based rpgs though so I didn't spend too much time on it. It is also made by square enix which I didn't realise until now.
Vagrant Story is most definitely an RPG. Maybe not really a western type of RPG like Dragon Age, but still very much fit for a role playing game.
Of course it's an RPG. There's character progression, stats, level ups, an upgrade system for your weapons and equipment, loot, a turn based combat system based around hit percentage and so on. It's definitely an RPG and a very good one at that.