With the contradiction between capitalism and socialism out of the way via the demise of the Soviet Union the first world has turned its attention on an underlying tension that existed but was submerged during the existence of the USSR: the tension between the freedom of the Third World for self determination and the desire of the first world countries to totally dominate the globe, exporting capitalist models of economic development based on neoliberal theories of globalization as well as western modes of dress, western culture, western languages like English, and western religious and political values.
The question is if the Third World has the right to determine itself in the face of this threat, which through globalization seeks to co-opt every culture and every country and, whether consciously planned and executed or not, integrate the globe into a single system of control with the first world on top and the formerly third world on the bottom as subjects. Subjects for economic exploitation as well as junior partners in westernization who, eventually, may be let into the club once they become either culturally white or western enough, "White" interestingly meaning in the U.S. roughly what "Western" means in the rest of the world.
If so, then what form might such resistence take? Cultural and religious resurgence perhaps, in the face of the media onslaught?
While September 11th was an awful attack and an awful loss of life, couldn't it be seen as an example of this Third World striking back at the first, as an event moving history and our current historical dilemma, that of the tension between western capitalism and the rest of the world, forward?
Neoliberal capitalism had been dominating the globe, the globe that had been dominated struck back, then of course western capitalism as embodied in the Bush administration and in the corporate power structure of the United States struck back at the Third world, first invading Afghanistan in the name of imposing western values on a regime that the west had determined had "Gone to Far" from its own values, then invading a blameless country for both the sake of establishing a beach head in a troublesome are to U.S. and Western global capital, the Middle East, and also for the purpose of positioning the particular U.S. capitals into a position to more efficiently exploit the Middle East.
Globalization teaches that there's no alternative to both unregulated capitalism and the growth of western cultural norms, the Third World strikes back, the first world even more explicitly declares that the rest of the world will have to go along with the West's standards or face military action against it.
I see the U.S. today in Iraq and in Afghanistan as representing the Iron fist behind the Velvet glove of globalization.
Now we have torture legalized, people held in legal limbo, in places where the United States won't let international agreements on treatment of prisoners of war be enforced, domestic spying, all internally, while externally we're expending lots of energy and money trying to keep a Third World which is increasingly going off the tracks of western integration in check.
It won't be able to do it forever; sooner or later, probably sooner, the chaos in the middle east will spread to other countries in the region, which may actually be a good thing in that increased instability there might open up the door to rewriting borders and political systems in such a way that the area is free from the heritage of 20th century colonialism as well as 21st century globalization.
To answer the question in the title, no, the first world does not in any way have the right to dominate the third, but you already knew that. Al Qaeda is bad but the popular frustration that groups like them tap into is very valid, a valid response to the world around them.
Hopefully more progressive organizations will come to the forefront that, even if coming out of a generally "Islamic" worldview, aren't conservative theocratic groups.