Well, I'm not sure how the XKCD version does it but if you draw a straight line from the middle of the map to your location and continue to the hour on mine it should match your system time pretty closely. The XKCD version doesn't create such a match for my time (even with daylight saving factored in).

Please let me know if that's not true for you on mine though. I'd like to fix it if it's wrong.