They do define what they think politics is. The article defines politics as exerting your will on others without consent. Thus, it's trivially zero-sum and we would probably all agree that it's not conducive to enjoyable spaces.

The main issue is that it's just a stupid definition. Politics in this sense is just one kind of violence. Most of the things we'd consider colloquially "political" don't meet this definition. Worse, many of the arguments that follow partially dispense with the given definition and unintentionally incorporate the author's implicit idea of "politics" (a separate thing), which makes it a bit confusing to read as a precise argument.