I remember learning about this as a kid from, of all places, a 1976 detective show called City of Angels (starring Wayne Rogers). Ten-year-old me thought it was so cool they would even broach such a topic on TV. As ways to become radicalised go …

This Video (French) says it’s a thousand years old, but that seems not to be the case, more like like 4-500 years.

I think the NYT is mistaken, as here’s an engraving of «jeu de paume» from the 16th C

According to the very long and exhaustive wiki

“The term real was first used by journalists in the early 20th century as a retronym to distinguish the ancient game from modern lawn tennis”, and, is it happens, 'It is also known as court tennis in the United States, royal tennis in England and Australia, and courte-paume in France."

I think the kings were pissed when they started playing tennis outside. “That’s not real tennis”, they probably said.

https://archive.is/rEQMr