Hello dude.
Yeah, this maybe just that UDK is not recognizing your custom gametype. You need to ensure that on your map, you go to UDK Menu View > World Info Properties Gametypes.
You need to select your custom gametype (with cover system, I think you are using PowerGame) on the supported gametypes for all fields (including PlayinEditor). Don’t forget to set yourgame type in the ini files, aswell the map prefix
However whenever you start UDKGame (not the editor), if you are extending UTGameTypes, it will always default to deathmatch (DM), so because this you can either change the ini files to make it load your gametype by default instead of UTGame, or you can manualy whenever start your game, change the game type on the menu, then select your map, and play the game.
It should work.
Take a look at this basic tutorial, however helps too much especially if you are extending UTGame:
http://www.hourences.com/an-entire-simple-udk-game/
It may seem simple, however helps a lot to understand how to setup your gametype whenever extending UTGame.
Cheers. 