But you are right that the author is mixing things up: Office politics isn't collaboration as described in the article. Office politics refers to things like one-upmanship, taking credit for stuff, playing the blame game - making yourself look good and others look bad, to get raises or promotions. Or for a phrase used in the article, office politics is about becoming a scheming backstabber.
It can also be the opposite.
Making yourself indispensable. Being the one who shows up for people (not as in "comes in and does a lot of unpaid work", but as in "helps out when other people need it"). Giving people credit where credit is due, especially the unsung heroes.
If you are well-known around the office as the person who is honest, kind, and helpful, the next time someone else tries to take credit for your work, make you look bad, or otherwise stab you in the back, it's much less likely to work—and when that kind of thing fails, it invariably makes the person who tries it look much, much worse.
Often times, doing the good stuff and building credit for that takes a long time and the right environment to identify and credit it.
Playing the politics game is much faster/easier and leads to quick results, because all you have to do is be visible as much as possible and manipulate a little bit here and there.
People aren't great at identifying the career manipulator and in the short term will give those guys the promotion/responsibility.