The thing that you're missing is that Microsoft used to ship that emulator with Windows. Then they stopped doing that.

AFAICT, Wine can run WIN16 programs. I don't know if it can run DOS programs. There's a WineHQ wiki page that says it can load DOS programs, but various internet fora seem to believe that Wine's DOS support is pretty broken. I've never tried it, and have no DOS programs handy, so I can't verify those claims.

There is also a port of Wine’s VDM back to Windows called otvdm or winevdm that is able to run 16-bit programs on Windows. It is surprisingly capable, I was able to run a 16-bit VB program that used a serial based optical modem without issue.

"DOS support" is tricky inasmuch as a lot software from that era - especially larger and more complex packages - interacted with hardware directly. In a sense, they weren't really DOS applications so much as they were bare-metal PC applications which were booted from DOS. It'd be difficult for WINE to support those, and other projects like DOSbox / 86box / etc do a better job of it.