"I do what I want."
Translation:Я роблю що я хочу.
Indeed, the audio doesn't have «я».
Both «Я роблю́, що я хо́чу» and «Я роблю́, що хо́чу» work here.
When the main sentence and the subordinate sentence have the same subject (я роблю, я хочу), you can omit the subject in the subordinate sentence even in the most formal texts.
(Note that this doesn't work for parenthetical phrases. In «Я ду́маю, я почита́ю кни́жку» 'I think, I'll read a book' «я думаю» is not really the main sentence: it's a parenthetical phrase. It doesn't really mean 'I hold a belief that I will read a book', it means 'maybe I'll read a book'. So, «Я думаю, почита́ю кни́жку» only sounds well in colloquial speech and certain contexts, but not everywhere.)