To quote the great Bob Nystrom's Crafting Interpreters, "Compiling is an implementation technique that involves translating a source language to some other — usually lower-level — form. When you generate bytecode or machine code, you are compiling. When you transpile to another high-level language, you are compiling too."

Nowadays, people generally understand a compiler to be a program that reads, parses, and translates programs from one language to another. The fundamental structure of a machine code compiler and a WebAssembly compiler is virtually identical -- would this project somehow be more of a "real" compiler if instead of generating text it generated binary that encoded the exact same information? Would it become a "real" compiler if someone built a machine that runs on WebAssembly instead of running it virtually?

The popular opinion is that splitting hairs about this is useless, and the definition of a compiler has thus relaxed to include "transpilers" as well as machine code targeting compilers (at least in my dev circles).