Does fair use apply here? (I don't know) It's not like the author narrates a full-blown wildlife movie with the voice of David Attenborough. It's just a funny demo which doesn't depend on the specific voice (could be anyone), and also makes it clear the voice is synthetic.
If you use a small clip of Brad Pitt in a 10 sec ad without his permission, he will probably sue you and win. So I don't think fair use is going to protect you.
Hold on, are we looking at the same video and Twitter message? [1] He clearly states what he's doing, and in the video he launches some program that appears to speak in Attenborough's voice. How clear is clear enough?