I maintain the owon.ro domain which uses a simple App engine app. I also we use google cloud dns.
These are the dns records:
A record with IP addres
Found the answer in the end thanks to Dan Cornilescu.
If you use Google Apps you can set up to redirect the naked domain to www.
If not, you will need to follow the steps by going to
Console > App engine > Settings > Custom Domain.
In here, at the second step, you will have to point www to the app (by using the second option) and clicking Add.
And then also point the naked domain to it by choosing the first option and clicking Add again.
So if I understand correctly you will server the app using www subdomain and the naked domain in contrast to redirecting the naked domain to www as in the Google apps case.
In the end, my custom domain tab looked like this.
And my DNS records looked like this