You (and others) should check out real time strategy games if your hope is to learn much of what you're sharing here!
Chess is a great game for removing all those external factors. It's just thinking
Not everything has to be an absolute competition-or-not. For the same reason you can enjoy a casual game of chess with a friend, you can enjoy a casual game of some RTS. Helps that there are a lot of open source RTS communities that each have their own skills-emphasis.