Was it entirely about the self-determination of the residents, British pride, enforcing international norms or was there some strategic importance to the Falkland Islands that popular memory has forgotten?
Domestic morale and straight geopolitics are widely acknowledged as one of the main reason the UK government reacted the way it did:
Although Argentina's forceful seizure of the Falkland Islands did not pose a threat to the security or territorial integrity of the United Kingdom, it constituted a loss of British overseas territory and also a serious blow to British pride and prestige in the international community.
The war did not benefit the British economy, it was arguably quite costly. Of course, the UK government did not consider the South Atlantic to be a high strategic priority. So the UK didn't gain anything substantial in terms of capital and/or the ability to exploit any additional capital. But it did make Thatcher more popular, enhanced Britain's prestige, and did allow parts of the British military to reassess itself through the experience of actual combat. So it's not like they didn't gain anything.
And the whole episode was certainly a major defeat for Argentina's interests. So the war is not entirely unimportant. The book also delves into some more interesting aspects of the war. Rare is the situation where two modern militaries (post WWII/Korean War), employing modern conventional military strategies (like air superiority), have faced openly on the battlefield. Certainly military types were watching very closely.