If you read the full article, it seems as if the Saudi religious establishment was infiltrated by Egyptian extremists fleeing a crackdown on the Muslim Brotherhood following the assassination of Sadat. Their ideology meshed with Wahhabism and Bin Laden's religious vendetta against the United States. The Saudi state apparatus did not have effective oversight over the religious establishment and so this all happened under the House of Saud's nose. The countries in red are (at the time) places with either US puppet regimes or some form of Arab Revolt descended, nominally secular/socialist regimes. The religious extremists pushing Islamic rule operated in these countries under various militias and terrorist groups, notably Al Qaeda, backed by the newly radicalized Saudi Wahhabi establishment, and of course, Iran.

From that perspective, the US was waging war against militias and terrorist groups with roots and support in Saudi Arabia, but the House of Saud was not considered to be complicit. The article goes on to say...

Astonishingly, the attacks of 9/11 had little effect on the Saudi approach to religious extremism, as diplomats and intelligence officials have attested. What finally changed royal minds was the experience of suffering an attack on Saudi soil. In May 2003, gunmen and suicide bombers struck three residential compounds in Riyadh, killing 39 people. The authorities attributed the attacks to al-Qaeda, and cooperation with the U.S. improved quickly and dramatically.

Interesting stuff, to be sure.