How will the club administrator get notification about membership request from user that want to join closed clubs?
I suppose you would get an email in your inbox on "my page", but I tried out the demosite, and no email was sent. If you are a moderator, then you can go to the moderation mode and accept club members. But you don't know when anyone has sent a request. There is a gadget (Community approval) at your dashboard, but this didn't get the latest approval request when i tested it on the demosite (http://relate.episerver.com)
You will need to create that function yourself. There are methods in the code for joining clubs and there you will have to add some more functions for sending emails if members are added. I you like you can send "real" email or your can just send messages inside EPiServer Relate to the owner of the club. But you will need to create that since it is not implemented in the demo package of Relate+
The approval gadget is only showing entitys that have the setting for approval set when created. Therefore they will only show up inside the gadget. Add members to a club is not the same as creating a new blogpost or club etc.
I do not have an example at the moment but you can probably figure out how to do that :)