I was surprised to see that TI had created this software for DOS. I don't know if it was originally paid software or if they released it for free (though it's so obscure now that I doubt anyone cares).
I've never used a TI-81 before, but the interface is very similar to the other TI calculators. As far as I can tell, this replicates the experience perfectly. The TI-81 is missing features that we take for granted in later models (nothing even approaching CAS or finding regressions, etc.) However, this has some really neat features that you normally wouldn't get with a physical TI-81. You can easily import and export programs to and from the DOS filesystem. You can print memory contents to your printer, which could be very handy. And you can also print out whatever is displayed on screen, both to a physical printer and also to a TIFF or PostScript file. Back when this was released, I can see that feature being extremely useful. You could, for example, embed a graph into another document before such a thing was commonplace!
I used this under DOSbox and it ran just fine, but your mileage may vary.