Manx is the demonym for people from the Isle of Man. It's odd to see it written "Isle of Manx" in a list of other demonyms, but the word Manx itself is far from modern. https://en.wikipedia.org/wiki/Manx_people

It's the Isle of Man to the best of my knowledge, but the people, and language, are called Manx. Like the English are from England.

Let's not forget the Mancs are from England as well.