No because "Swiss cheese" means "Emmentaler", not "Schweizer Käse". Quote from the article:

> In the U.S., we call it “Swiss” cheese, while in Switzerland, it’s known as Emmental.

Well, that's the point of the OP, isn't it? Emmental cheese is one of over 500 types of cheeses produced in Switzerland, but by calling this one product ("the") Swiss cheese, you're kinda implying that these hundreds of other cheeses that are actually also produced in Switzerland do not exist.

It's a bit like: "In Germany, they call this car a BMW, but here we call it German Car."