Ohhh. I was trying to play it singleplayer, my bad. Thanks bro!

Are you running it from the server browser? It is a coop mission, so it can only be played in the multiplayer part of arma although you can play it solo and private without being accessible to anyone else.

If you haven't launch the multiplayer browser, here's how:
Launch Arma. Once it's started select 'multiplayer' then 'server browser'
At the top select 'host server'. A list of settings will show up. Look at the 'HOST' option. If you have it set to 'LAN' then it will be a private game. Click the 'Host Server' button.
Next you can choose the map on the left, and the mission on the right. So click 'Altis' on the left and you should see 'Ground Breach' on the right. Click it then click 'play'.

How do you play this gamemode? I downloaded the map but I can't find the option to play the gamemode anywhere.