When people say "no politics" they mean have a position on certain issues that mostly are off topic in a business environment.
For example if I have my group where nobody is religeous. You could rant about how stupid religeous people are because nobody would feel particularly attacked and some would nod along. Disregarding that the pittyful self-revelation from pointing at others calling them stupid, this is a political stance.
But we employ people from all over the world and viewpoints change. Some don't have the most dense main stream belief you find everywhere. You don't go into the next office and pronounce how atheism is the best thing. That is meant with "no politics". It is a requirement for multi-cultural exchange without immediate conflict. It is of course not restricted to religion.
The auther misunderstood what politics means. What he describes is office and relationship dynamics. There is quite a bit of overlap, especially when it comes to signal your viewpoints and perspectives in the hope to get recognition. I would be careful about that in a professional environment though. Depends on the company and how many cultures meet each other in random watercooler talk.
You can convolute the terms here, but it just blurrs the precision of any statement.
That said, relationship dynamics or "power play" leads to an effect where the most competent people often aren't the most well liked people. That is unfortunate and not very new. But the problem cannot be adressed by "talking more about politics". On the contrary, it would make things much, much worse.