No, they don't. Only two controls these days use the parallel port. Mach3, and LinuxCNC. You don't need to use the parallel port with either one, but you'll need additional hardware, which adds additional cost.Do modern CNC systems need a parallel port
While that machine may come with a Mach3 license, technically, Mach3 licenses are not transferable. But it will still work just fine. And a Mach3 license will work with any version, even the latest (which is still 5 years old).
The best low cost option to use Mach3 without a parallel port would be the UC100 controller from CNC Drive. It's just over $100, and provides a parallel interface for your existing breakout board and drives, and connects to the PC via USB.
CNCdrive - motion controls