I didn't look at what format the "database" is in, or if the size would make it (im)practical to simply zip it up and email it around, but if the format isn't readily consumable by non-technical people, there wouldn't be any reason to not utilize a tool like git anyway.
`git clone --bare` is enough.
- hosting on AWS is not free for super high traffic (assuming the free tier can't keep up) - serving files from S3 is not free (though it's cheap enough at low read levels, it adds up)
At a typical level of traffic, the author's current host may be sufficiently inexpensive. Assuming the author was assuming many, many times the usual traffic (even if everyone is kind enough to bare clone), it would be a pointless expense.
Of course, third party hosting can take the content down... and this is where git became relevant. Assuming the author was more interested in distributing the content than the prestige of being the distributor, even though Github etc. took down the repo, every person who has since cloned is now capable of re-publishing to any new upstream repository of their choosing, on any server.
Assuming, again, that all of this was the goal, it probably made sense to utilize the free, fast, scalable third party hosting as long as possible rather than risk self-hosting slowing down or collapsing under traffic, or creating a massive spike in cost.
That's a whole boat load of assumptions, any of which could be wrong. In the realm of possible motivations, though, I think it's a fairly logical conclusion.