The language itself is a fairly typical FP, but only if you disregard the VM it runs on and the OTP framework.

As I've frequently said about Erlang, the language is much more powerful than the sum of its parts. There are a great deal of complementary features in the stack.

It is really the BEAM that is most compelling, Elixir is a great language on top of it, but the VM provides tools that simply don't exist in most other languages, if any. Specifically things like runtime tracing with pattern matching, the ability to connect an interactive remote shell to a running system and poke at it using code, ETS/Mnesia, hot upgrades/downgrades, etc.