Once it’s updated, you can check all your passwords against the list. It’s a list of sha256-hashed passwords.(so he isn’t sharing tons of plaintext passwords, as sha256 can’t be reversed) You would sha256 your own passwords and check them all against the list.

Edit: to clarify, I think there are tools to help check against the offline list pretty easily. Or you could also query Troy hunts pwned password page (or its api)once it’s updated; instead of downloading 9gb. The k-anonymity model is pretty clever, and querying the site should be secure.