It seems like there might be a middle ground, like being willing to play the game, that doesn't imply being "a servile cog?"

The trick seems to be knowing when the game is worth playing. There are certainly situations where competition is too fierce and requires too much preparation, so it's not worth doing if you don't really enjoy the game.

I'm not sure getting hired at a large tech firm is quite that competitive, though? They do hire lots of people all the time.