Guys, I do understand that this is an additional layer of this game. But there are more than enough layers. The game is really sophisticated. Some of the layers may be excessive. Don't you find?
I hope this makes my words sound more reasonable: Right now I am in the Top10 at the 5th place with 1801 rating. So, it is not the case when a player loses a lot and whines: "Let's make this game simpler."
For example, yesterday I had a game when a player at my left side (let's name him "A") started to attack me from his 3rd move like a kamikaze. The player at right ("B") promoted a pawn to a queen on his 5th or 6th move (because my opposite player ("C") was too passive and ignored all what happens.) So, from the 6th or 7th move "A"+"B" attacked me together. As a result, "B" earned some points by eating my pawns and pieces at the right flank while I protected the left flank from the "A" kamikaze. In the meantime the passive "C" (who should be my "friend", because his army is in front of mine) woke up and got a second queen. At the very next move he checked "A"'s king with his brand new queen and "A" immediately resigned. Neither "B" nor me had any chance to eat the "A"'s king faster. So, "C" got +20 points and an advantage (he had the whole army). It is not some rare case. I believe any of the 1700+ players will confirm that.
Does "C" deserve those +20? He just checked the king once. "A" could protect easily. But he resigned. The only his motivation was to attack me and then make a +20 gift to some other player. To anyone but me 
Renegade_Yoda suggests to point bishops towards the enemy kings. Did I have a chance to do that? Definitely no. Now let's imagine that after "A" resignation his army is controlled by AI. In this case I could protect my right flank from "B" and then either help "C" to finish that "A" pest or at lest be ready to steal a checkmate.
This is just one example of many.
Suggestion: Leftover kings, etc.
@BabYagun your initial algorithm is incomplete. You must also handle the case where...
5. If no squares are left in the list then...
a) ...the zombie king is in stalemate, nobody takes points!
b) ...the zombie king passes. He may move again at his next turn.
c) ...the zombie king moves to an adjacent square controlled by more that one player, if such a square exists.
d) ...the zombie king moves to a random adjacent empty square, if such a square exists.
e) ...the zombie king moves to a random adjacent square. If the square is occupied by an alive piece, the piece is captured by the king.
f) ...the zombie king is transformed to a zombie knight, jumps to a safe square, and now has a value of only 3 points. lol!
Well, you are right. I just did not want to spend too much time thinking about this algo, because was not sure someone is going to use it. Now BattleMind told that he may create the AI some day. So we may keep posting our ideas. Including a zombie king actively looking for other kings' brains.
Why only kings? The brains of queens are also delicious! lol! 
Since a zombie does not possess a perfectly functional brain, I expect for it to charge at alive targets with delay. Which means that the AI algorithm should not run before his next move, but after his last one. The direction to where the zombie is intending to move next, could be indicated by a small arrow. So all human players would have some information, to base their plans for killing the zombie.
@BabYagun, Your example to me seems laser focused (but true). In part that same example would put you in same bad spot with changes as well your still down boxed in and can't come up for air since the players you are playing against choose to do what they did (I think we can agree more than likely because you were high ranked). That said your point is valid.
I really like your over arching comment about lets make the game similar (coming from a high rated player that means something to me).
I am not saying I agree what I am saying/thinking it maybe that is where the discussion should be see if the admins/group can agree on the overall game should it be simpler or do we want to more chaos what's this variant best chance of global success (fun and addicting would be my two founding pieces). If we at least understand where the game is going then the suggestions will (hopefully) better align with that.
I agree, we need to understand the strategic direction: should we simplify the game or make it more chaotic some way (maybe with rolling dices ) or maybe we need 2 (or 3) different variants. Would be good to get some feedback from the developers. How do they see the future of this game.
I agree completely with that post @Renegade_Yoda