According to that article, the Aramaic word for God was also something similar: "Alahah". I would hazard a guess that this may be the origin of the word "Allah" in Arabic. Aramaic is a much older language than Arabic, it became the official language of the both the Assyrian and Persian Empires. It is well known that Muhammad was heavily influenced by the proselyting of Christianity that was going on during his life, presumably it was mainly done in Arabia by Aramaic speakers seeing as they were located nearby and their language is somewhat related to Arabic.
Also the Meccans are said to have had another name for their supreme diety: Hubal
I would suspect that the word Allah came to Arabia via Aramaic, and Hubal was an older word for essentially the same thing. A chief God, sort of like the role that Zeus played in the Greek Pantheon.
Nevertheless, even Hubal may be of foreign origin, as it is clearly related to the Phoenician Baal, which was the chief male God of the Phoenicians/Caananites.
Interestingly, the name of the Ancient Greek supreme deity Zeus is similar to the modern Greek word for the Christian God (θεός).