using System;

using System.Linq;

using Newtonsoft.Json.Linq;

public class Program

{

    public static void Main()

    {

        string json = @"

            {

              ""910719"": {

                ""id"": 910719,

                ""type"": ""asdf"",

                ""ref_id"": 7568

              },

              ""910721"": {

                ""id"": 910721,

                ""type"": ""asdf"",

                ""ref_id"": 7569

              },

              ""910723"": {

                ""id"": 910723,

                ""type"": ""asdf"",

                ""ref_id"": 7570

              }

            }";

        JObject jFoo = JObject.Parse(json);

​

        string[] refIds = jFoo.Properties()

                              .Select(p => (string)p.Value["ref_id"])

                              .ToArray();

        Console.Write(string.Join("\r\n", refIds));

    }

}