In the Chamorro dictionaries, there is no word "chilenko."
I am always suspicious that a nickname, unless obviously derived from other sources, is based on a Spanish word.
There is a lake in southern Argentina called Chelenco. But that part of the country is so isolated that one wonders what possible connection it could have with the Marianas?
There is a Spanish word cholenco. It means "a hybrid, a mix of two species, whether animal or vegetable." Applied to a mixed breed dog, it means "a mongrel."
I wouldn't be surprised if chilenko comes from "i chilenko" from cholenco (hybrid).
Don't forget that our mañaina were very much exposed to and influenced by the Spanish language as we are today by English.
But it's just a guess how this branch of the Arceos got this nickname.