Do groups of men who are friends engage zero-sum status games? What do those look like?

Aren't most status games zero-sum, though? Would I be right to assume that you meant the kind of status games where the men of Group Y are trying to raise their status at the expense of each other rather than those not in their in-group?

If so, almost any form of social interaction in a given group can have zero-sum status game elements. As an example, the simple act of sharing information can be construed as promoting one's superior knowledge and thus showing the other guy up.

You mentioned the saying "Men insult each other and don't mean it. Women compliment each other and don't mean it." That's definitely a working example of such games. Here's an extract from Duels and Duets: Why Men and Women Talk So Differently by John L. Locke, via Google Books:

Although duels abound in adolescence, and in the oral cultures that anthropologists love to study, they may erupt wherever competitive men congregate. Playful insulting occurs everywhere that men go. In the early 1970s, anthropologist Frank Manning spent some time in a black bar (or "social club") in Bermuda. One thing that stood out about the male patrons was their insulting, especially the artful and friendly way that they did it. Since there was always a responsive audience of men and women in the club, Manning thought these verbal exchanges could "be viewed as spectator games and public performances," opportunities for the participants "to display their personality and style for the benefits of an audience as well as their competitors."

While Manning was observing the black duelers in Bermuda, E. E. LeMasters was busily at work in a white working-class tavern in southern Wisconsin. LeMasters, a sociology professor by day and patron of the "Oasis" by night, noticed a great deal of banter in his natural laboratory. In fact, some regular patrons light-heartedly attacked each other more or less continuously. In the Oasis, social success was dependant on men's "ability to 'dish it out' in the rapid-fire exchange called 'joshing,'" wrote LeMasters. "You have to have a quick retort, and preferably one that puts you 'one up' on your opponent. People who can't compete in the game lose status."