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.