At a large company, your job after a certain level depends on your “impact” and “value delivered”. The challenge is getting 20 other teams to work on your priorities and not their priorities. They too need to play to win to keep their job or get that promotion.
I would not say it’s about getting other people aligned with your priorities instead of theirs but rather finding ways such that your priorities are aligned. There’s always the “your boss says it needs to help me” sort of priority alignment but much better is to find shared priorities. e.g. “We both need X; let’s work together.” “You need Foo which you could more easily achieve by investing your efforts into my platform Bar.”
When you are higher up, that is when you become said good boss, or that boss's boss, the dynamics of the grandfather comment kick in fully.
Impact is a handwavy way of saying “is your work good for the company”.
Of course a group can also have bad actors but that’s not really an issue with politics specifically. Politics are neither good nor bad.