"A compiler takes in a stream of symbols and translates it to another stream of symbols. Common compiler techniques include intermediate tree representations, parsing of symbols, various recursion-based optimization passes on the intermediate representation and phases, and various serialization techniques."
The second sentence is a good definition. The first sentence is probably the cause of the disagreement -- it's so vague as to possibly describe a C compiler, as well as a Chinese Room, a signal detection algorithm, a kid doing his math homework, etc. I'm not quite sure what you call something that transmutes a stream of symbols into other symbols that is precise, but i feel "things that transmute symbols" covers a very broad class of things that are not compilers as well. Someone doing their chemistry homework, for instance.
I mean, yes, a compiler will transmute symbols, but it's the second sentence is how we distinguish that from, say, a DSP. When you start asserting things like "builds an intermediate structure representing the parse tree", then the definition starts going somewhere useful.
"Necessary but not sufficient," and all that.