This makes sense, and I even thought it might be a good idea to think of Assembler (the program) as an interpreter rather than a compiler: each line of code can be seen as a command to emit a piece of machine code, allocate space, change state or mode, etc.
The assembler is not an interpreter because it doesn't produce the output of the program it assembles.
However indeed it's usually called a translator (or, well, an assembler) rather than a compiler, exactly because its algorithms are simpler, and (even if it does things like resolving labels) the way a human looks at the output is as a 1:1 translation of the input.
It produces the output of running the program it assembles under the nonstandard semantics Koshkin is suggesting.
I think assemblers are not called "compilers" purely for historical reasons: they existed for a decade or so before compilers, and initially the "compiler" was more like what we would call a linker (thus the name "compiler").
