You could use a simple WebRequest and parse the JSON to get the emailAddress field.
You could build a Response model that would look something like:
public class APIResponse
{
public string emailAddress {get; set;}
public int messagesTotal {get; set;}
public int threadsTotal {get; set;}
public int id {get; set;}
}
Then you will want to make a GET Request to the GoogleAPI url and deserialize the JSON response from your API Response class.
WebRequest request = WebRequest.Create("https://www.googleapis.com/gmail/v1/users/me/profile");
request.Method = "GET";
request.ContentType = "application/x-www-form-urlencoded; charset=utf-8";
request.Timeout = 50000;
//Get response from server
using (StreamReader stream = new StreamReader(request.GetResponse().GetResponseStream(), Encoding.UTF8))
{
sResponse = stream.ReadToEnd();
resp = new JavaScriptSerializer().Deserialize<APIResponse>(sResponse);
}
Then you could get your emailAddress back by simply calling resp.emailAddress.
I have not tested this code for the GoogleAPI but this should get you going in the right direction.