I don't have any actual experience with Data East/Sega/Stern transformer connectors but experience from Bally/Williams can be applied here.

It looks like the transformer has a Molex series 3191 plug (https://www.greatplainselectronics.com/proddetail.asp?prod=19-09-2159).
It looks like the cabinet has a standard Molex connector plug (https://www.greatplainselectronics.com/proddetail.asp?prod=03-09-2159).

I can't tell if the pins on the transformer side are male or female.

I don't think it will matter which series of connector you use - as long as they mate.

Molex series 3191 https://www.greatplainselectronics.com/proddetail.asp?prod=19-09-2159 mates with https://www.greatplainselectronics.com/proddetail.asp?prod=19-09-1159 as far as I can tell.

Standard Molex series https://www.greatplainselectronics.com/proddetail.asp?prod=03-09-2159 mates with either https://www.greatplainselectronics.com/proddetail.asp?prod=03-09-1154 or https://www.greatplainselectronics.com/proddetail.asp?prod=03-09-1157 according to GPE's website.

If you re-pin you should either take a photo (or note) which color wires go where and make sure they match up. The colors and voltages are described in the manual on page 95 (that you have a photo of above) in case you're confused. If you want to be extra sure measure the voltages to check they match the manual specification before mating the connectors and powering on.