I'll disagree only a tiny bit here: To me (also a compiler engineer), a transpiler is shorthand for source-to-source translation from one language to another at a similar level of abstraction (e.g. Lua to Ruby, Java to C++). The implementation of a transpiler meeting that definition is generally a simpler project than a compiler, by virtue of the fact that you get to offload a lot of things to the compiler of the target language. That doesn't mean they aren't incredibly complex in their own right though - compilers are just enormously complex projects for anything approximating a production-ready toolchain. Anyone using the term as a pejorative should be laughed out of the room.
In any case, I 100% agree that this is obviously a compiler. The fact that the compiler emits WASM as text, i.e. WAT, doesn't mean it is source-to-source translation - the output is still assembly code for the target machine.
And as an aside, does it really emit WAT? or is that just a debugging view of its output? If you can emit WAT, there is zero reason you can't emit WASM too.