tl;dr Play the game. Watercooler politics mean more than your code when it comes down to who gets promoted.
Why all the stuff about hiring? As an engineer, hiring isn't even your job. You may end up participating in the interview process and offering feedback, but ultimately you're not making the hiring decisions unless you're a manager anyway, so ignoring hiring isn't really a mistake you make as an engineer.
It's not just about getting promoted. It's much easier to get things done when you work well with the people on your team. And the more influence you have because of those connections, the more influence you have on hiring decisions. Keeping a bad team member from joining your team is huge.
Why all the stuff about hiring? As an engineer, hiring isn't even your job. You may end up participating in the interview process and offering feedback, but ultimately you're not making the hiring decisions unless you're a manager anyway, so ignoring hiring isn't really a mistake you make as an engineer.