I believe you can just use a small flat head and a little force. Power off.

Marco sells one as well.

https://www.marcospecialties.com/pinball-parts/77-IDC156

Yes, it would definitely be a .156" IDC punchdown tool. Pinball Life has it for a decent price:

https://www.pinballlife.com/0156-396mm-idc-wire-insertion-tool.html

Playboy display connectors are 0.156" crimp type, not punchdown type. I don't live in the US so I'll let others comment on best local source for crimp tools.

But it's not common for those female display connectors to play up - it's much more common for the solder joints on the male pin headers on the displays for those connectors to fracture/crack. Pull the displays out and carefully inspect the soldering on the connector pin headers first - resolder any bad joints.

Much better price.

If you do only a few connectors then the Mascon tool (MRT-156F) as pointed to by Ken is a good choice. Downside to the Mascon tool is the plastic bit. These wear down over time. One thing to consider about this tool is the manufacturer is now defunct. As supplies dry up, they won't be replaced - if you like this tool then don't wait too long. I haven't ever found any good alternatives to these at that cost point.
The Molex version has a metal bit which will last longer - 63813-3503. Downside to the Molex tool is a higher price.

I'd probably change those to crimp type but I have plenty of 20 pin blanks of that type (since you have to redo them all anyway.)

IDC has its place.... in network and phone cabling! I hate it for everything else.

Those idc.conns are 40 years old. I replace those when doing a restore as they will continue to have problems.

Bally games of that vintage should be 100 % repinned. Eliminates lots of weird issues and gameplay is alot better.

Got pictures? I'm curious if they're factory or if someones just retrofitted them.
My Playboy's in the middle of the production run with crimp connectors. First game I've seen with IDC was Silverball Mania released a year and a bit later than Playboy.