がる and がっている can indeed be used to talk about yourself, because this construct essentially talks about outward signs indicative of someone's internal thoughts, emotions, or feelings. So it's all about the appearance upon which certain conjectural conclusions can be drawn, either by the speaker or by someone else in the speaker's mind.
So 富山はケーキを食べたがっている literally means: Toyama is showing signs that tell us Toyama wants to eat cake.
I am sure at your level you have read or been taught that the reason you don't say 富山はケーキを食べたい is that you don't know that; you can only observe and make speculative statements based on the signs you observe.
How does that figure in a statement about oneself? It's the same idea. You are talking about the signs you give off because of a mental state, thought, or feeling and how those signs might affect other people. See these examples:
Note : Basically you use がる ( = garu) for the third person but there are some cases you can use がる ( = garu) for yourself when you see the actions or emotion objectively in certain conditions.
= He bought me the bag I really wanted.
= Did you know that I really wanted to study Japanese?
= I shouldn’t be keep feeling sad. I should move forward.
Also this explanation:
がる TO TALK ABOUT YOURSELF
While the most common usage of 〜がる is to talk about others, it can also be used to talk about yourself. In these cases though, you are not describing your internal state, you are describing your behavior and how it affects others. Here's an example of how this looks:
When I show that I want snacks, my sister always shares her snacks with me.
In this sentence, the main focus is on your sister, and the fact that she shares her snacks with you. I wish my sister would do that for me! We used 〜がる here to indicate that you are behaving in a way that alerts your sister of your need for snacks.
Important note: this usage only occurs in subordinate clauses. Please see @aguijonazo's comment.
Edit: Overlooked 俗物的
俗物的, 形容動詞 (na-adjective), just means worldly-minded or materialistic. Here it is used to contrast ストイック meaning someone who's not swayed by fame and money. 俗物的, in this instance, is its near antonym.