He didn't remove anything, the word "typically" is used in your second sentence for a reason, because it's the most common example.
They are emulating the server software (not the client, which is freely downloadable for all anyway) and it is a perfectly acceptable use of the word. Yes, you'd typically associate the word emulator with things like dolphin, or any virtual machine in general, but the use of the term emulation is perfectly fine in this case regardless.
If the end goal is to behave exactly like another program in every imaginable way, then it emulates that program. It (attempts to) communicate with the client just like an official server would, and manages to trick the client into believing it is connected to a real server. Textbook emulation.
Usually your posts actually have some basis even if I think they are based on completely false premises, right now you're just embarassing yourself.