Man, I totally took the punchline for granted. Then again, my dad once designed golf courses for a living, and although I've only been to a few hoity-toity country clubs, you can't show up for any decent tee time in denim, sneakers, or a t-shirt. You have to be properly attired. That's what they mean by a collar -- just like jough said, it's a collared shirt. And you CANNOT wear regular shoes on a green. Once you understand how hard the maintenance guys have to work to keep that green looking pretty, you simply must wear cleated golf shoes. Your nasty old Reeboks will crush the grass and ruin the hell out of it. The cleats help keep the grass looking decent and playable for the next party.
Nobody wears a button-down oxford shirt on the course, that's just ridiculous. Fellows and ladies change out of their workaday clothes and into golf attire for a day on the green.
Golf to today's culture is what tennis was in the '80s. Sure, you can head on down to the local community center and learn how, but there's a certain way that polite society has to throw down the special rules. Hence the attire.