Yes it will work. The reason you see mention of the
FireCuda connected with gaming systems like PS4 & Xbox as well as laptops is because of the 2.5", 7MM height form-factor. The gaming systems require that form factor and almost all laptops do as well. They all connect the same way, via SATA cables, so they're perfectly fine for use in a desktop.
The
2.5" verson of the FireCuda spins at 5,400 RPM (Revolutions Per Minute), which is considered slow for desktop. Good news is the FireCuda also comes in a
3.5", 7200 RPM version as well, might be worth looking into that. It will perform better and is more suited to your desktop. There usually isn't a large gap in cost between them either.