I don't think this way of analyzing a character tells you the whole story.
When you describe a character without mentioning their appearance and occupation
It can be important to mention a character's occupation in order to demonstrate how the character relates to that occupation. "She is forced by circumstance to be a bounty hunter, as it's the only job she's qualified for, but as a pacifist and a rebel sympathizer she constantly experiences internal conflict." This begins to describe a complex and interesting character in a way that someone who has never seen Star Wars would understand, but it still mentioned the (imaginary) character's occupation.
I also think it's unfair to discount wardrobe as part of what makes a character interesting. Clothing and style are a large part of any person's identity, and movie characters are no different. Perhaps more so since a director and a costume designer choose wardrobe very carefully while considering what a character's clothing conveys about their personality and their circumstances.
If I were to simply say "You know Princess Leia, she's the one with the cinnamon bun hair," just to get my non-Star-Wars-watching friend to realize who I was talking about, then that would be a shallow and uninteresting description - but to me that doesn't mean that the character is shallow and uninteresting. Mentioning the character's clothing and occupation in order to describe them appropriately shouldn't disqualify them from being an interesting or complex character.
(n.b.: I have not seen the review you are referring to, so I'm not sure if this answer addresses your question completely. But this is my opinion on whether or not that's a "correct" way to analyze a character. And let's also keep in mind that I don't believe that there is only one "correct" way.)