That sounds like Service Merchandise. It has been over 20 yearsWe used to have a store around here called "Consumers Distributing" that worked the same way, but it wasn't just electronics, it was all sorts of merchandise. My mom used to take us there as kids. You would walk in, and there would be tables with their catalogues on them. You would go through the catalogue, fill out a paper with the item numbers of the things you wanted, then take it to the desk, and they would go and bring you all your items.
I just checked online, it looks like they declared bankruptcy and shut down in the mid 90s.

We used to have one of those A&W places nearby though I never went in there, It closed a couple years ago and has since been replaced by Dutch Bros Coffee which seem to be popping up all over Austin in the past year.