Same here, and I've been trying to understand it too. I think it's a combination of things.
Objectively, the MiST has two main advantages over the rest: an "instant-on" authentic feeling and an extremely low power consumption.
Some might not care about the first, but the latter can be measured and is an undeniable advantage: it uses ~2.2W, which is less than a Raspberry Pi (~3W) and a Chinese NES clone (~3.3W).
In my book, this low power consumption means it is a better
machine than the original - because it needs less power to do the same task
[of course compatibility needs work but it will get there]
Then perhaps more subjectively: the MiST being open-source means we can tinker with it, and it was kept at a (relatively) low cost by a judicious choice of connections (I prefer USB over PS/2).
This makes it a good machine to mess around with - EXACTLY like the old Amiga and Atari machines back in the day which inspired the demoscene and other creative endeavors.
Some of the above probably applies to other FPGAs; but the final bit is that the MiST uses an Altera chip which seems to have many owners (as dev boards), which creates a good base of potential developers.
I think this is why we have 13 cores running, with (hopefully) more to come as people get inspired to try something new.
So basically... beyond just running the software (which we can do in emulators), it is an amazing little piece of hardware