Truly "digital" joysticks, in the DOS realm, can be thought of as Atari joysticks--simple 4-directional joysticks with a single fire button--that can be connected to the computer. The appeal of such setups was the elimination of joystick calibration; with digital joysticks, you're either pushing the stick, or you're not.

Some companies, like Banana Software Development, supported this setup, although you had to build a simple device to attach the Atari-style joystick to the parallel port of the PC. Some other computers supported "digital" joysticks natively, like the Amstrad PC.

Joystick (Digital) is part of the Input Devices Supported category.