He writes that the region is not very important to the USA. It's not, but it is a strategically important area, not only in terms of its location, at the nexus of Asia, Africa and Europe, but also because of the oil there. Now the US is not dependent on Middle Eastern Oil, but Japan, China and other countries are. So controlling the region will mean a lever of power over those regions.
The U.S. is dependent on oil and the oil market is global. Even if the U.S. is a net exporter of oil, Americans still pay increased prices for pretty much everything as a result and the economy suffers. The only way around this would be a scheme in which domestic oil producers are forced to sell to American refiners at pre-war prices, similar to the "National Energy Program" that was tried in Canada during the '80's. (Spoiler: It didn't turn out well.)
Yes, the U.S. is less likely to see its pumps run dry and U.S. oil companies are going to be very happy with the increased prices. However, unless it goes the NEP route, U.S. companies are going to export more oil creating shorter supply at home. Americans will pay the same high prices everyone else will be paying. As we're seeing now, the U.S. might actually see even higher price increases than countries like China.