The segmented control is used to group like buttons together.
The control is native to Mac OS X  and seems to be native to GTK+ 3 as well , being used for e.g. navigation buttons in Nautilus . For Qt, see http://stackoverflow.com/questions/3610234/create-capsule-style-toolbar-controls-in-qt . Windows don't seem to offer a native control, but Microsoft still uses it in e.g. Office 2007 .
This kind of control is important for visually grouping related commands 
as well as separating tabs from content area when appropriate , and is key to furthering LibreOffice's UX.
 I'm not exactly sure what GTK+ 3 offers. Buttons that are part of the "inline-toolbar" class (http://stackoverflow.com/questions/9855671/python-gtk3-treeview-buttons) display this way, as does GtkStackSwitcher.
 Such as in https://wiki.documentfoundation.org/images/5/5a/Impress-tabs.png from the UX guidelines -- https://wiki.documentfoundation.org/Design/Guidelines
Valid enhancement request -> NEW.
This appears to be very similar to notebookbar.