A Z-abuse is, simply, an abuse of the Z-machine.
To elaborate: The Z-machine was designed solely for text adventures. It is not a platform well-suited for videogames or any other programs that require single-key entry, graphics, and split-second timing. Some people see that as a challenge.
The first and possibly best-known Z-abuse is Freefall (porter: Andrew Plotkin; 1995; Z-code), which is an Inform port of Tetris (Alexey Pajitnov; 1985). Carl Muckenhoupt, a.k.a. baf, said in a late review that "it's difficult now to fully appreciate the amazement and horror that the idea originally inspired." 1
Since then, many other non-IF games have been ported to the Z-machine with varying degrees of success. Where graphics would normally be used, ASCII graphics are used instead.
The Z-machine has had more abuses written for it than other IF platforms, but a few abuses have been written in Hugo and TADS as well. The TADS-abuse I'm Gonna Take You To The Video Bar! (James Mitchelhill; 2004; TADS 2) is particularly noteworthy, since it plays a video animation done entirely in ASCII graphics.