Handshake is a blockchain which wants to replace existing DNS registration system. So when you want to look up example.com, instead of consulting IANA's database for "who owns .com", you consult the Handshake's blockchain.
The zooko system uses a "hack": since, this is blockchain, there is entire past history on the chain. So you can keep repeatedly updating a random field (like a TXT entry for some domain) and use equivalent of "git log" to read the entire timeline.
This will need a special client, which will parse blockchain for such updates, but everything on blockchain needs a special client, so not a big deal.
Re "5 million users" -- this is a very good point, and yes, if this takes off this will be significant problem for Handshake blockchain. I suspect this is the core of disagreement between Zooko's author and designers of the Handshake blockchain ([0]).
From the point of Handshake authors, Zooko system uses blockchain resources, but does not help with main mission (make Handshake team super rich by taking over existing DNS system).
From the point of "publiush", there is this Handshake blockchain which has authentication solved, and it can be used for all sorts of fun stuff. The fact that this was not original intent just makes it more fun and exciting.
https://news.ycombinator.com/item?id=29912944