Just to expand a bit on the progression: it works because iii and vi sound a lot like I.

E.g. in they key of C I (C E G), iii (E G B), vi (A C E). iii can be seen as Imaj7 without the root (C) and vi as Iadd6 without the 5th (G).

So basically this is I-V-I-I with some decoration, being V-I the quintessential movement in western classical music.

I listened to Romilda Gebbia if that was what you were refering to, and to me it sounds like I V vi IV.

iirc those are the same "4 chords" used by the Axis of Awesome [1]. Certainly sounded like that to my ear from memory, but don't really have enough music notation/theory knowledge to know for certain and I may have been mis-remembering.

[1] https://www.youtube.com/watch?v=oOlDewpCfZQ