Lisp user here. I couldn't see what he was talking about re: "Elixir is a Lisp" and the "why" was pretty hand-wavy, but the author does seem pretty stoked about whatever he/she saw so good for them.
It has the interactive features for inspecting and modifying a running system that Lisps often have.
It has reflection APIs
Its ints are big like Lisp
etc.
Seems pretty Lispy to me.