Everything is asynchronous but the linked article uses the synchronous versions of the functions for some reason... async versions exist and are recommended[1]

[1] https://github.com/ncb000gt/node.bcrypt.js#async-recommended

Do the async methods actually execute on a thread pool though? Or do they use enough async methods internally to periodically release the main thread enough to keep it responsive?

From a quick glance at the source, the answer to the first is no.

This one is truly async, it uses a libuv managed thread pool.

Yep you're right - disregard what I said above. :)

asynchronous doesn't magically make CPU-intensive tasks faster.

It does mean other tasks (e.g. serving pages to visitors) can still be run at the same time as the CPU-intensive task though, like most languages do when it comes to hashing passwords and logging people in

Correct, but it sure does stop your entire single-threaded process from blocking to the detriment of all other requests.