What the heck is that

It's definitely an aftermarket radio. Clar was a radio manufacturer, although I can't find any online information about that specific radio (they seemed to be more into tabletop models). Someone probably upgraded/changed the radio because of the different frequency bands in Europe. The factory AM radio would've worked in Europe (MW, I believe) but LW is a different standard than the US. If the car was imported when it was new, it's doubtful that Chrysler would've wired a Euro radio through a parts-store fuse holder when there was a fused radio circuit already in the car. Of course, I can't speak to the dealer's actions.

You could try to disassemble the fuse holder and replace the fuse (5A should be plenty) if you want to keep the vintage radio, but I would instead suggest removing it from the car and testing it on the bench with a low-amperage 12V power supply. Testing it on a car battery could cause a fire if it's internally shorted.