Maltese is definitely its own language. Arabic roots are there (theres a Semitic joke in there ) but it isn't arabic anymore. Its written left to right with a variant of the english alphabet.
Hindi and Urdu are 90% the exact same language, and are mutually inteligible (Urdu speaker and Hindi speaker can have complete full conversation with each other) but each is written differently (one LTR the other RTL) and with different alphabets
In my books, the distinction between languages and dialects are so arbitrary that the best method is simply to ask the people that speak those languages/dialects. If they consider them to be different language (which Maltese speakers seemingly do) I call them different languages.
I don't buy the argument of just asking the speakers. There are cultural, political, etc. reasons people may think things which don't conform with reality. Many Hindi-Urdu speakers get insulted by the reality that the languages are pretty much the same because they don't want to identify with people from another country their country is constantly at war with.