I am wondering what this type of secondary global navigation is called - it is always placed above the global navigation. Since my organisation is thinking about implementing it, I would like to read up on research (and best practice) into this type of navigation.
It sounds like utility navigation to me:
A customer may want to look up the shipping date of an order, peek at their wish list, or pay for their purchases. That little row of useful links is often called utility navigation. It provides access to subsidiary tools that help the user, but it is not the core reason for the web site.
Einstein once said things should be simple, but no simpler. This screenshot you have included within your post is a for a large company. You have several menus on that page. Products on the left, a drop down for products (top left) and then the global/site navigation on the top-right. Notice there is yet another navigation menu at the very top, on the left and right, for the users account details.
A site of this scale does not want to mix/confuse the user with products, site-specific navigation and user account navigation. So they group it within the same place, hence the menu above the menu (your question). They are grouping links that are similar, and so they should on such a huge website that probably has around 1,000 pages.
My feeling is if your site is not a huge one, don't put a menu next to a menu. Spread out the content. It is commonplace now for the 'Contact Us' style links to be placed in the site's
Not sure there is a name for those navigation links.
Many sites, when implementing the selected IA (Information Architecture), choose to present few links up-front instead of 'hiding' those inside the menu. Its all about discoverability: they are just easy to spot without digging into the menu. (you can read this NNg article about navigation here)
Whatever you choose to do: test it with users, or have analytics to see if people notice those and use them.