False.
Nowhere in the OT does it say to carry out war forever, or until all people are subjugated. It was always with a specific goal in mind, then it would stop.
Islam is a syncretist religion, like Mormonism and a number of other odd heresies. Its founder had a "vision" that incorporated certain things from the religions found in his environment: practices from his own paganism, including the name of his god and the black rock with its vagina-shaped fertility symbol in Mecca; Levitical law from the Jews, along with the concept of a religiously dominated state (although Mo was a theocrat and Judaism had never been a theocracy, strictly speaking) coupled with a bit of OT conquest talk that the Jews had long understood as symbolic; and the Christian concept of a non-racial, non-geographical, non-bloodlinked religion that grew through proselytism.
Granted, his idea of proselytism was based upon the sword and force and violence, totally opposed to Christianity. But essentially, he was a syncretist who just happened to come along at the right time in the right place, when the Roman Empire had fallen, the Church was weakened by the Arian heresy, and there was no one to oppose him. It would be like having L. Ron Hubbard take over the US.