I think this misses the central idea in the essay - it's not that nerds are arrogant for thinking they are above social games (they're not), but that nerds are "nerds" because they prioritize the pursuit of knowledge over the pursuit of popularity (in broad strokes).
In fact, nerds would very much like to play the social game and be at the top of the ladder, but at the stage in life being discussed (high school), nerds don't have the kinds of life experiences or knowledge to play the game well, precisely because they spend most of their time tinkering/hacking/learning about other things.
I think there's another part of the equation as well. The market(HS Students) is valuing its peers by what type of value they can provide each other TODAY. It's NOT DISCOUNTING each other for future value, because the students don’t know what will be valuable in the future (ie more resources), or don’t care(they’ll never see each other or too short termed thinking).
It makes sense that football players or cheerleaders would have more perceived value since they can unite the school at events. If theres a football game friday night and the team wins, the student body immediately benefits. Jocks are also more likely to be physically fit which signals a strong potential mate to females. Although being physically fit seems like it is the number 1 indicator for providing resources, we find intelligence takes the cake later in life.
As PG stipulates, nerds focus more attention on being smart because they enjoy it more or look to reap the future returns (more opportunities, more resources). Either way, nerds focus more value on being smart. Nerds are not above social games though. As they tend to become extremely valuable for the short and long term, you see the ones that want to get ahead ‘play the game’. Look no further than Silicon Valley for proof.
But most nerds want to be smart as a proxy/substitute for being popular. This isn't necessarily bad, as reallocating "popularity" based on "intelligence" rather than "secondary sexual characteristics" seems like a beneficial thing for society. But they are not monks, squirreled away reading books. They compete, they associate, they judge others who would be the "smartest." It's the same game, different arena.
In fact, nerds would very much like to play the social game and be at the top of the ladder, but at the stage in life being discussed (high school), nerds don't have the kinds of life experiences or knowledge to play the game well, precisely because they spend most of their time tinkering/hacking/learning about other things.