"Backstabber" refers to somebody who is a traitor or hypocrite or someone who says bad things about someone, without them knowing. What the word means is a person who attacks ("stabs") you when your back is turned (When you are not aware of them doing it). So, in the context of the example, you could succeed in office politics by saying bad things about people, behind their back, to make others think they are not a nice person. This means you turn people against each other. The example is saying it can help you succeed without this. I hope this helps.