first make sure it works on the test mode of construct2. To do that, first u have to go your google play dashboard ->game sevices->select your game->on the bottom of screen u will see the name of your game in blue color. Clic there.->You are now on developer console. Clic on credentials on the left of the screen. (i know u know that. I say just in case .
And u have to put the client ID on construct2´s GooglePlay plugin.
Well... When u run test mode does it works??
If the answer is yes, when u export to intel cordova u have to fill client secret too on googleplay object of construct.
Now export to cordova. Open Intel XDK.
And remember add the plugin of google services.
To do that u have to add plug- ins from third parts, and, on the text box white: com.intel.googleplaygameservices (If u prefer, u can use the plugin checking the box on the intel xdk plugins).
Sorry for my bad english.
Tell me if now works