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.
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.