Email Notifications not going with Cron job

I have a site set up on Siteground. I have a cronjob set to run every 30 minutes and I'm pretty sure it is running regularly. Users mentioned that they were not always getting notifications, so I looked in my EasySocial control panel and saw over 400 messages waiting to go out!

I plugged the cron URL into my browser thinking that should send some of the messages. It doesn't seem to change the queue - at the front end or at the back end of the queue.

Output from the cron url is:

[{"status":"200","contents":"There is nothing to dispatch currently.","time":"2015-07-30 23:26:10"},{"status":"200","contents":"Current photos storage is set to local.","time":"2015-07-30 23:26:10"},{"status":"200","contents":"Current photos storage is set to local.","time":"2015-07-30 23:26:10"},{"status":"200","contents":"Current avatar storage is set to local.","time":"2015-07-30 23:26:10"},{"status":"200","contents":"No files to upload to Amazon S3 right now.","time":"2015-07-30 23:26:10"},{"status":"200","contents":"Stream archive disabled.","time":"2015-07-30 23:26:10"}]

How can I get these notices moving?!!!