I have recently bought a Toshiba Tecra 750CDM and am waiting anxiously for it to arrive- I don't have the port replicator, but I assume that as long as you configure the game/MIDI port in BIOS, it should be accessible directly from DOS without any need for driver, as usually the software you'll be running will take care of talking to it.

Have you tried checking out your BIOS config?
I don't have any gamepads or MIDI devices I could test unfortunately, but I can try and confirm if there's any setting for the game/MIDI port in my BIOS and get back to you. I figure since they're similar laptops, the BIOS should be pretty similar to one another.

I just got my Toshiba Tecra and I was able to check the BIOS (before it stopped working, unfortunately) and there's no settings for the game port in it- I would give it a go if you own the port replicator.