You are correct, the "Arduino language" is just C++ with some special libraries, macros, added types, and an IDE that enforces some limitations on the programmer (though you can use the Arduino library without the IDE).

In practice using this library/ecosystem/whatever is different enough from "normal" embedded C/C++ libraries that to me at least to me it does feel like a different language.

I think most people call it a language out of ignorance or laziness though.