I'm not sure where you're seeing such a menu like available. Looks like you had a menu like to GJs allcategories page then you changed the plugin in the dropdown to GJ Events leading behind the &action (Joomla isn't very good at clearing these unfortunately).
No there is no all group events page or anything of the sort. Yes, such a page is planned at some point, but I've no idea when, sorry. Only solution would be to build out your own such page as a custom component.