I'll say that docs are delightful to read and beautifully explain the domain. I would recommend going through them even if you never use the ZMQ itself.
I remember reading the ZeroMQ docs when I was first learning about concurrency. Those plus Joe Armstrong's Programming Erlang book were really fun and eye opening.
I never used ZeroMQ much but it taught me a lot of the language around distributed and high-concurrency systems and problems that come up.
Not OP but if you're on the edge, try reading the first few chapters of the ZeroMQ guide. It does not make a lot of assumptions about the reader's background in computing.
Yes, nothing else comes close. The nanomsg author seems to have abandoned nanomsg.
Typically software infrastructure like 0MQ, ext2fs, Valgrind, HotSpot, and gzip takes about a decade to get good, remains optimal for a decade or two, and remains relevant for half a century after that. A couple of years is not a long time.
I never used ZeroMQ much but it taught me a lot of the language around distributed and high-concurrency systems and problems that come up.