There seems to be a conflation of the TWO Gulf Wars.
		
		
	 
They are directly related. It's perfectly reasonable to consider them one war, with an intermission. 
It was all about the US trying, in her usual unsubtle and inept way, to engage in gunboat diplomacy - sending a message to the world that as undisputed top dog, she can beat down any opponent with ease. 
Similar conflicts during the Cold War just turned into long, bloody, and pointless slug-fests, as the two superpowers did everything possible to support whichever side the other hadn't picked, short of actual direct conflict between the superpowers militaries. 
Nobody wanting to start WWIII didn't mean nobody wanting a war, it just meant they were fought by proxy. 
Remember when the Mujahideen were on our side? They were the good guys, because they were fighting against the Soviet Union (they even helped James Bond to escape from a Soviet airbase in Afghanistan in the 1987 film 
The Living Daylights). Not at all like the evil Taliban, who are sworn enemies of the USA. 
The fact that the Mujahideen and the Taliban are mostly the exact same individual people, still fighting for the exact same reason (to rid their country of interfering foreigners) seems to be lost on most people. We have always been at war with Eastasia.
The end of the Cold War meant that suddenly we had to pick our enemies for different and often more sensible reasons than their mere allegiance to the USSR. The crazy Islamic fighters in Afghanistan were never the natural friends of the West - but in the Cold War, the enemy of my enemy was always my friend. 
Of course, nobody thought it really mattered too much - it was inevitable that sooner or later the war would turn hot - at which point we would all discover we had a few minutes to live. UK civil defence was a complete joke, based as it was on the expectation of just three minutes of warning of a nuclear strike. As we used to say in the '80s, at least that's just enough time to make a nice cup of tea.
An interesting demonstration of the different views of the Cold War between West Germany and the UK can be found in popular culture - specifically the song 
99 Luftballons released by Nena in 1983 in Germany, and then released in English in 1984, as 
99 Red Balloons. 
[youtube]http://www.youtube.com/watch?v=La4Dcd1aUcE[/youtube]
[youtube]http://www.youtube.com/watch?v=mqrqfp6agug[/youtube]
Both tell the tale of a nuclear apocalypse, but in the German version, this is sparked by greedy politicians who believe that they can gain personal advantage from a war; while in the English version, the war is sparked by paranoia, with the military incorrectly believing that an attack was underway, and launching in retaliation. 
It's an interesting diffence in perspective, and says a lot about what the two nations were most concerned about at the time. 
In 1983, 
Stanislav Petrov singlehandedly saved the world, when he refused (against orders) to launch a retaliatory strike after his air defence system reported multiple ICBM launches from the continental US. It turned out that the Soviet satellite had in fact detected the rising sun reflecting off some scattered clouds. So this idea of an accidental global war was really not particularly far-fetched.