I would say tactical negotiation and leveraging personal connect is healthy, but manipulation for personal gains at the cost of a larger good is what is my definition of "politics".
I have seen couple of managers in my career who, while were poor managers based on employee voice surveys in the company, ended up with large charters due to being good at politics/"rubbing backs". I want to say that end result was they screwed it up since their directs ended up leaving their team, but in reality, they thrived despite losing folks and not delivering projects, again due to politics. As an engineer, I failed to appreciate that.
Now, if you're a good politician with the best interests of the company at heart and the technical skills to deliver, the math is different, and the sky's the limit for you :)
I think that's an unhelpful definition; one should avoid conflating the activity with a particular goal. Politics is governance and decision-making, and how to convince people to support your position; whether that's performed for personal gain, or for the good of the company, or for the good of society (and the three are not mutually exclusive), is another thing.
This means developing empathy for other sides of the business, building up favours from other teams, forging alliances, listening, gathering intelligence and spotting trends.
at some point, you _will_ have to make hard decisions, your budget will be cut, project killed, etc, etc. If you are a skilled "work politician" you may be able to negate some, or all of the bad effects.
tl;dr: s/"Avoid politics, but have right folks vouch for your work"/"Become an adept politician".