This is just a clothing-knowledge based guess, but I expect they would unfasten on the same side as, say, a double-breasted suit (http://en.wikipedia.org/wiki/Double-breasted_suit) coat. So, unless the photo on that page is a fluke or a woman's double-breasted suit coat, it'd be his right.

As for how it unfastens. That costume probably predates regular use of velcro. Most likely it fastens with a snap, or a button fastened to the back side of the strip that goes through button hole on the tunic.