Their search backend is, in my experience, significantly faster than you'd expect of latencies through a typical app backend - request-to-render in 10s of millis or less. They run their search indices directly inside an nginx module, it's an interesting architecture to read up on.
The JS they kick you off with is a pretty decent way to make a thorough, not-trivial search experience, you can get much more than a list of results (faceting and such builtin)
(https://community.algolia.com/instantsearch.js/)
The all-over-the-world bit is an optional part of paid plans, it's quite possible HN isn't using the global DSN
The vast majority of the JavaScript is superfluous third-party libraries like AngularJS. The actual app is under 2,000 lines of code. I do not expect it would be difficult to cut the frameworks out of it at all, for a lighter and faster experience that only weighed a few kilobytes.