At first I do not want to touch the engine! However, I do not see anything in the game that allows you to build or publish the game you're working on.
As marauder2k9 said, you can use the pre-compiled version.
Actually you don't build the game, it's already build (pre-compiled) unless you compile from source, that you only need to do once, again, unless you modify the source.
What do you mean "publish the game"?
There are several methods you can use for publish the game. But actually is pretty easy, basically you can compress your project game folder with zip, 7zip or rar. That's it. Then you can share the game in any method that you like, the other person only need to decompress and then run the game.