The Pointy Stick Game was a game played by the boys from the Dwarf. ("Legion", Series VI)
The game involved pinning a pointy stick on a TV Weathergirl (presumably the one from Groovy Channel 27 mentioned in "Psirens").
When the Dwarfers met the talented savant Legion, Arnold Rimmer contemplated trying to convince Legion to join them. Dave Lister said that Legion wouldn't join them, and wouldn't fit in playing The Pointy Stick Game.
Rimmer pretended to have an interest in fine art, telling Legion that the Dwarfers sit up every night discussing it, and Cat said that the Pointy Stick Game doesn't get a look in anymore.