Usually when you say "emulator" people think there's an inherent performance hit because of a fetch-decode-execute interpreter loop somewhere. Reimplementations of things don't have that performance hit even though they are lumped under the same umbrella as actual interpreters and recompilers.
Related note: if WINE is an emulator why isn't Linux or GNU? They both reimplement parts of UNIX, which was even more proprietary than Windows is today.
On most of these architectures the software eventually executes as x86 machine code, and the distance between x86 machine code and the actual processes inside a modern CPU implementing the x86 code set is so vast you can call a modern CPU an "x86 emulator built in hardware."
I mean, it depends on the context. I don't think it would be wrong to say that Linux "emulates a UNIX environment" or some such, which is closer to what OP actually wrote about Wine.
You've probably used a "terminal emulator" at some point today. ;)
In regular joe-schmo parlance, an emulator would be something that translates a hardware machine into software that is run on a different machine. Hardware being the important word here. Performance has nothing to do with how people use the term emulator in regular parlance.
Related note: if WINE is an emulator why isn't Linux or GNU? They both reimplement parts of UNIX, which was even more proprietary than Windows is today.