Midway uses those male/male things within their wiring harness to allow the control panel to be disconnected from the JAMMA wiring up at the control panel area. The actual part Midway uses is made by Panduit, and I don't know where to buy it in the USA in small quantity, but you can just use a pin strip with long pins on both sides if you want.
Try
Digikey S1232E-36-ND (long, tin),
S1022E-36-ND (shorter, tin),
S1231E-36-ND (long, one side gold plated) or
S1021E-36-ND (shorter, one side gold plated).
Those are each 36 position headers, but they easily break-away (snap) to whatever smaller length you desire, and you can make multiple pieces out of each one if you need more than one connection. If your connectors have pins missing to form a keyway (Midway normally did this), just cut the necessary pin out with some wire cutters or flush cutters.