However, I have no idea why anyone would want to emulate Cyrix chips or later PCs other than out of curiosity. A lot on this list does seem superfluous.
Gaming, mostly. A lot of computer games from back then simply will not run on modern machines. Even after things fell into place with DirectX/OpenGL, Windows is such a complex system that keeping all those millions of plates spinning at once is simply impossible
There's games today that I can't run from the last 15 years alone, like Westwood Studios Command & Conquer series. The company is defunct, and the buyer (EA) lost the source code over a decade ago, if you believe the rumors. There's simply no other way to RUN the game past Windows 7 (EA no longer bothers patching it to work on newer systems with their re-releases)
The only alternative is really to simply buy the older hardware, which is becoming increasingly scarce and difficult to maintain (why would we keep these 30 year old Video card drivers says someone at AMD, before rm -rf'ing them off the FTP for instance?)
Maybe one day I'll get adventurous and see if Windows 98 will run on DosBox.