There is an arcade stick.
It has an electronic PS3PS4 Fighting Board.
Mortal Kombat 4 understands the buttons of the controller, but does not see the crosspiece of the stick.
How do I make the game understand the movement of the stick?

Don't have that hardware, but MK4 sees only the analog X/Y axis, so if your stick is recognized as a "hat" / "dpad", it won't work with the game.

There's 2 known ways to fix this issue.

1.- Use a software that maps stick movement to keys, like this:
https://github.com/AntiMicro/antimicro/releases/latest

2.- Use a virtual joystick (doesn't work with PS4 controllers):
https://www.gog.com/forum/mortal_kombat/using_dpad_for_control_instead_of_analog_in_mk4

With some controllers or arcade stick, you have a selector that allows you to tell the computer to detect the hat as an analog stick (for instance, 8bitdo and Mayflash sticks do that, as well as the Hori Fighting Commander gamepad).

By switching on the "cross is left analog" setting, that should fix it.

Also if your controller/arcade stick has a DirectInput mode, switch to it and MK4 will manage it much more smoothly.