Although there can be other monads (and stuff other than monads, such as ZipList) that can be made with lists, I think that such a monad would not necessarily b

Although there can be other monads (and stuff other than monads, such as ZipList) that can be made with lists, I think that such a monad would not necessarily be a "list monad". (Your link [1] has several examples of this.) You are right that it does not mean that "a list is a monad" and that your other phrasing is better, but it does not mean that "there isn't a list monad".