Not true. We sell them all kinds of stuff, but not enough to bring back all the dollars that go over there now with $60 oil. But we do sell many billions of dollars of American products to Islamic countries: Boeing airplanes, SUVs, luxury cars, construction equipment, tons of oilwell equipment and services, chemical plant equipment, movie DVDs, music CDs, etc. It's just not enough to recyle all the petro-dollars back to America, so the remaining dollars return here through purchases of corporate stock and real estate.
It sounds like the writer is oversimplifying Cheney's positions on "social issues." For example, it might actually reduce our influence on the Sudan if we stop trading with them.
"We sell them all kinds of stuff, but not enough to bring back all the dollars that go over there now with $60 oil."
Maybe that was basically the point of his comment---"nothing to sell them to get the money back."
Most likely he's aware of the sell of items from the US to Islamic states.
"For example, it might actually reduce our influence on the Sudan if we stop trading with them."
Not true at all, from a psychological or economic perspective. Trade is a reward that sets up a positive-reinforcement cycle of encouraging negative behaviors. Their government has more money, and can acquire more efficient means of persecution.
The US has a 700 million dollar trade surplus with UAE, not a deficient.