Mark, the car is actually there to call attention to a folkart store in that building. So, you can't hire it, but you could make your own. All you need are 1) assorted cans of spray paint; 2) assorted teenage boys; 3) an old car. Wrestling mask is optional.
The kid in the mask was friendly & willing to answer questions, though somewhat hampered by the fact that the mask had no mouth. I asked what the car was & he said it was a '61 model. I said that I thought it looked older, that those lines were from an earlier era. He said, in his muffled way, that he was pretty sure it was a '61. I pointed out that I could remember 1961. He was genuinely taken aback -- "You can?!" ;D That must seem like the very distant past to him.
Strangely enough, and only a little off topic, around the back streets of Cairo are many old and abandoned dusty relics from the 60's and 50's. There was a ban for many years on exporting cars (why, I've no idea) and so many just got left where they fell.
Never having owned a car, I don't really know much about them or even have much interest in them. But, living in Paris, I have noted that something is definitely happening in the 21st century with the number of cars plugged in... or displayed in the BMW showroom next to my office.