Saudi Arabia has the fifth largest military budget in the world. They spend more than Germany, France or the UK. Their training and readiness probably isn't nearly as good, but to say they have no military is ... odd.
More to the point, many nations sell oil for non-USD. It's quite common. Further, the oil trade is a small fraction of international USD movement. The idea that the "petrodollar" is a major factor in international politics is... unlikely to be true.