Just defending my idea some.
Why does using the map to sneak around work...because of a few things.
1)In the heat of a battle between two or more people, are you really going to have the time to look at the map to make sure somebody else isn't coming. Yeah, you can do a quick glance, but if you spend too much time, then you get attacked and can't fight as well.
2)You missed one of the options of the map. When you are AWAY from the action you can click and actually watch what is going on from your map screen to see how much damage people have and such. Then decide if you want to get into that battle.
3)Using the Map touch screen for teleports and such. Do a teleport move and jump behind somebody as they are trying to attack another character. Even if they did see you on their map by the time they see you on their map again you can already have an attack going.
4)Powerups and special moves can hide you from other peoples maps. Cloaking device will actually have a purpose. How about an attack that scrambles the use of other characters maps. It is all possible to be done.
My ideas are sound if you execute them well...and spend time to think about how it would work in the grand scheme of the game.
Some people were talking about having 2 arenas to fight in that you can basically watch at the same time, but how is this much different than a normal level, except that it is on two screens. So I can throw you down to the other screen, unless both screens only have limited interaction with eachother then that idea isn't revolutionary it is done before.
The map idea adds to the mix of having bigger levels. (Always a plus.)
Map based powerups like transports, missle locks, mine placements, I am sure you can think of more.
Map-enhancing or dehancing attacks, where you can render the player with a disadvantage with an attack hurting the map.
Last, with the map and larger levels it will make the game more viable to play with 8-16 players. Add into the idea that everyone has their own screen and the system could push more enemies and such going on you could even have more enviromental hazzards and such.