It's true that SpaceX has enjoyed a string
of recent rocket successes, including the fact that Elon Musk's rocket company broke through into the market for supplying space launches to military and defense clients. But a monopoly? A monopoly is what existed before SpaceX entered the market, when the United Launch Alliance (ULA), a joint venture of Lockheed Martin and Boeing, was the sole provider of military launches for more than a decade.
What Paul is on about is the new National Defense Authorization Act (NDAA) for fiscal year 2018, which the Senate is considering. According to his op-ed: