It may not be an emulator in a highly specific & technical sense used by and useful to a small group of experts. It is an emulator in the general and widely-recognized sense of "software that runs software originally intended for a different, incompatible system."
You see this all the time when a jargon word enters the general non-specialist vocabulary. It doesn't make either usage wrong, though it can be confusing sometimes if the contexts can be difficult to distinguish. In this case that's unlikely so just give it up please.
Honestly the quirk where that is its name could be a really useful entry point for educating non-specialist readers on the different technical approaches used to solve this problem! I never see that though, this is only ever used as a wellackshully on internet forums. It sucks.
Honestly I don’t even understand the narrow sense in which you could say WINE is not an emulator.
There was supposedly a naming discussion in 1993 which resulted in “WINE is not an emulator”. Maybe this was to remind people that you still needed an x86 processor (WINE is not an x86 emulator), or maybe it was born from the idea that WINE does not emulate Windows—maybe it “provides a compatibility layer” or “reimplements the Windows interfaces”.
The Windows APIs are not so well-specified that a mere reimplementation of them would run so much software as WINE does.
