Mame maps some discreet controls as anolog in mame (12 way joysticks are another example) You need to convert the digital values to analog to use the control in mame. I'm building an interface for a 12-way rotary to do this at the moment. It's still in the design stages, but I can add support for your guns.
From the schematic the gun puts out a 3-bit grey-code. It doesn't use 0 0 0 so there are 7 possible gun positions:
(Pad 1, Pad 2, Pad 3) 1=gnd
1 0 0, 1 0 1, 1 1 1, 1 1 0, 0 1 0, 0 1 1, 0 0 1
Grey code:
http://en.wikipedia.org/wiki/Gray_code