I was having this problem too and finally figured it out - it is a combination of settings in your preferences and a line that you need to copy over from config.default.php.
Copy this to your config.php and replace the 9 with the ref of the user group that you want to get email notifications (the name of the group won't work here, it needs to be the ref number):
$email_notify_usergroups = array("9");
Then go into your preferences for Actions and disable showing resource requests in your action list (the first item in the list) - if this is enabled the emails will not be sent:
I believe this preference will need to be set individually for each user. The other settings in your screenshot look fine and shouldn't affect this.
There may also be some interesting options available in config.default.php if you search for $email_user_notifications - this area of the file has all of the variables relating to user notifications and how they relate to email.
Thanks,
Adrian