Either we're talking about the same thing and have a communication problem or I very well might be a minority when it comes to deep reflections on my experiences - something I never considered before. I would define art as any aesthetic that is life-changing or enriching. Every single video game that I keep in my collection has either changed my life (Kid Icarus Uprising, Passage, Braid) or has enriched it (Zelda, Metroid Prime, Mario Bros.) through gameplay alone. I have one final example if you're willing to watch it (it's only like 7 min long).
I never looked at missile command that way, as Albicant said that is purely a risk management game for me.
I get your point though with a game like Civilization. That taught me a lot about the world and how I would want to rule a country, and at which point I would sacrifice democracy to get rid of an annoying threat. Yet I don't see decision making as part of the art. It's no different then playing a complex board game.
One game in particular has completely changed my life, caused me to move to another continent and marry the girl I met in game. The game mechanics made that possible, yet I don't credit that towards the art of the game.
I guess we have different definitions of what art is.