REST is just a style of API. You can write a JSON API that isn't RESTful just as easily, and in some cases a RESTful API is not warranted.
Fox Sports has a pretty restful XML API. I can't remember if it's SOAP specifically, though.
SOAP is a bit weird because it's both an envelope/delivery mechanism as well as a discovery/interface negotiation methodology.
REST is just straight up a set of interface design principles. It doesn't care what you're delivering, it doesn't care about the channel you deliver it through.
He's saying they aren't perpendicular and also saying they are independent.
REST is a tool. But given an engineer a tool like a hammer and pretty soon everything will look like a nail. Sometimes you need a screwdriver when you actually have screws. Hammering them in will work but it is ugly.