It's sort of implied that it's not Burp Intruder, but Burp Intruder would be a pretty normal way to do this.
It's actually Burpsuite, you can tell from the screenshot he provided.
He's using Burp Suite for things, but writes about "fuzzing" for directories as if he's not using Burp for that (the plural on "tools" sort of suggests he's using something like dirbuster).
Dirbuster, gobuster, or some variant is probably what was used here.
Brute forcing is not fuzzing, neither of those are fuzzing tools
Yeah that's what I thought. Fuzzing doesn't discover API endpoints