I think all the links that stay on the same domain should always open in the same tab. Outside of the domain should open in a new tab. There are other ways to open it in a separate tab or window.
Though for a mobile experience it is harder to open something in a new page or tab. So it would make sense there.
I wouldn’t put the menu on a hover though. And I also think the color of the icons is a bit too much attention grabbing.
I can already hear managers talking about different icons for outside and inside links. :O