Hey, all, some good suggestions so far, and a few that I would like to address.
I think that making empty spaces territories is a good idea. Perhaps they could only attack the four squares around them, giving all but 4 places (A1, B1, G1, and A2) access to a chess piece. Then, if you own the king and queen of a color, blank spaces of that color give +1, and chess pieces of that color give +2. Note that it is still possible for the map to have only 26 territories, but the 64 territory idea sounds pretty good.
I had thought about it earlier, and I want to avoid the 4-player chess idea. The point of this map is to be unique, yet remain familiar and have mass appeal. Surely many more people have played 2 player chess than 4 player chess, and I think the 2 player version would be more well received.
Also, negative troops for off-colored territory will not work, because you would have to evacuate your king and queen of the same color (assuming that you own them) to attack the enemy on a different color. That would be awkward.
Also, regarding the pieces being continents by themselves, that seems biased towards the player that starts off with a king or queen, because they get a +10 or +8 from the get-go. (I'm really shooting you down here, aren't I, Keredrex? Sorry...)
Anyway, I would like to know whether the legend on the bottom (the one showing the movement of pieces) is necessary, because removing it would save space, and possibly eliminate the need for scrolling.
I also want to know if further graphical work needs to be done on this map, and who should do it. Since the only graphics program I have is MS Paint, this is about the extent of what I can do, aside from a background image and some more colors. I suppose this should wait until all the good ideas are implemented, but it might be necessary if this is ever going to become a real map.
Thanks for the support, and keep the ideas coming.