It's not a database, it's just files. And they are hosted by Cloudflare so they can cope with a lot of downloads.
I think he should make the files smaller my removing the second half of the hashes, i.e. reduce it from 40 hex digits to 20. This increases the change of a false positive (i.e. I enter my password, it says it was compromised but it wasn't, it just has the same hash as one that did) from 1 in 10^48 to 1 in 10^24 (per password), but that's still a huge number. (There's less than 10^10 people in the world, they only have a few passwords each). This will approximately halve the download, maybe more because the first half of each hash is more compressible (when sorted) the second half is totally random.
"Oh you want your own copy? Sure, just thrash seven shades of shit out of the database. Here's how."