The term "playing politics" or "play politics" is an idiom. An idiom is a figurative meaning as opposed to a literal meaning. After discussion with others...It's apparent that most do not know what a politician is....beyond the most basic meaning of an elected official. I am sure that much weight could be added to that on a broad base.... beyond this forum....more so in fact:)
I'm quite sure most don't realize that Sheriffs and Judges et al Magistrates ..etc are elected in many jurisdictions through a political process..which in turn makes them also...politicians.