Look at the last picture of the XLR output - there are screw grooves on the inside rim. That is VERY old school. I had a Shure mic in the early 70's that had the same thing; the XLR cable didn't click in, it screwed in. The mic is probably about 35 to 40 years old if it does not have the standard click in XLR connector - good luck finding cables for it.
BTW, if it is a screw-in type a standard XLR cable will fit, but it will not click in firmly, so it could fall out with just a small tug or after even being jostled several times.