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. Input devices supported by games in order to enhance gameplay or offer alternate way of controls, but are not necessary in order to fully play the game.