You're presuming compiling means taking the source code and producing machine code, low-level codes, etc. But compiling actually just means taking one source code and turning it into another. So it seems reasonable to say that taking Typescript and producing JavaScript is a form of compiling. It's not dissimilar to what (for example) c# does when its compiled into IL language.
That said, I'd say a better word for this is Transpiling. I'd suggest that the Typescript compiler is better described as a Transpiler.
The difference is subtle and a transpiler can be thought of as a type of compiler; but a (pure)compiled language is (usually) turning a high-level language to a low(er) level language (nearer to machine code), like the C# example. A transpiler turns a high-level language into a similar level (of abstraction) language (also high level).*
The result of the compiled code is typically not a language that you would write yourself. The result of a transpiler is another high-level language. In theory, you could write IL (as an example) but it's really designed to be produced by a compiler and there are no tools or support for doing this, you produce IL by compiling C#/vb.net, only. Whereas Javascript is a usable (and used) programming language in its own right.
*Lots of caveats as the definitions of these words and their usage are pretty vague
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