Reply to myself.

I was able to fix it. But the solution is really stupid. It seems, since a few versions now, the MAME developers have dropped the branded controller files from the distribution. So I needed the x-arcade.cfg file.

I was lucky. I still had MAME version 0.85 laying around on a disc here. That version still contained the necessary controller file. So by copying this 6KB (!) file, I was able to get it working again.

What where the MAME developers thinking by dropping these controller files from the package??? Surely package size issues are not a thing here. The entire /cntrlr directory contained 5 files for a total whopping 29 KB!