OK I downloaded the map and now I see what the problem is. I think I know how to do it.
First summon and armor stand {Invisible:1b,NoGravity:1b,Marker:1b} at every coordinate where a block could be. The use execute + detect. For example:
/execute @e[type=ArmorStand] ~ ~ ~ detect ~ ~ ~ diamond_block ~ ~ ~ execute @e[type=ArmorStand,c=1] ~ ~ ~ detect ~ ~ ~ diamond_block ~ ~1 ~1 execute @e[type=ArmorStand,c=1] ~ ~ ~ detect ~ ~ ~ diamond_block ~ ~2 ~2 execute @e[type=ArmorStand] ~ ~ ~ detect ~ ~ ~ diamond_block ~ ~3 ~3 say Diamond won.
This command first detects if there's a diamond block at it's location, and if it is, it detects again at the nearest armor stand (itself) if there a diamond block at it's diagonal, if it is, it detects one block further again etc. You would near four commands for four diagonals and for each team.
And just one more suggestion:
/effect @a 23 2 100 true (true at the end cancels particles)
If you want I can try to implement the changes to the map and send it to you by email, unless you want to make the map yourself, I would understand that.

plasmo321gmail.com

/title @a title {selector:"@p[score_win_min=1]", color:green, extra:[{text:" won the game!", color:yellow}]}

This is how you display someone's name in text, also works with tellraw and subtitle. You can change /title times if you want the title to be displayed for a longer/shorter peroid of time.
I haven't downloaded the map so I don't know what scoreboards, teams etc. you uses in your map, just change whatever you need to change in this command.