I assume Pulstar is one of the GOG ports. I do not own it myself, but I own King of Fighters 2002, Blazing Star and Ironclad. All are playable with a gamepad. The game is sadly just not telling you about it and only shows the keyboard layout. However, you cannot remap the buttons. That is not really a problem for me, but maybe for other people.

I have it and it works fine with an XInput pad. It uses SDL so I suppose it works with DirectInput controllers as well. Just don't use the keyboard to navigate the menu otherwise the pad will be set as the second player controller; also when the game loads press Start to enable the pad (insert coins with RB).