Part of the nomenclature problem here is that there's no other way to refer to an HTTP-based API. REST was originally an alternative to the horrible SOAP. I'd be fine with calling it something else (because the author is right, nobody's following Fielding's vision), but there's nothing else to call it.

"JSON-over-HTTP(S)" is a bit verbose, but accurate.

HTTP API?

The author suggests RESTless.