I don't think it has anything to do with your handedness, but rather what country you live in. Walk down a sidewalk in America...you'll notice that you, and most likely everyone else, walk on the "right" side, just as if we were driving. This occurs in department stores, grocery stores, etc.
As I mentioned in that old post, we covered this in psychology class - specifically amusement parks and other large events like fairs, carnivals, flee markets, etc. Left handed people in America still drive and walk on the right side, so it doesn't have anything to do with hands.
However, with all the guidebooks and lure to E-Ticket attractions, this has thrown off the natural flow in most cases, even EPCOT. We've started with Mexico and Canada, both, and it's the same result.