The problem with the tutorial you linked is that it is outdated and does not work.
There is information in the tutorial which does not exist but is required...
If you can find me the: 'Client Secret', I will stand corrected.
Here is the quote from the tutorial entry:
The client secret for the game from the Google Play Developer Console. This is only necessary when publishing via Cordova (e.g. PhoneGap Build). For more information see the section Setting up Google Play Game Services above."
This is the official manual written by scirra. If you feel it's outdated you must tell Ashley or Tom
However I still recommend you to use cranberrygames Cordova plugin. I own the package and yes, it takes a while till he response, but he will update his plugins.
Moreover I never have had any issue with the Google Play Games plugin so far.
It's worth for giving it a try.