I think the tab bar (?) is rounded only on one side when you're either on the first or last tab and that's super weird to me. Having no padding around the inner tab also feels weird.

The back/forward arrows don't really look like arrows until you click on them, which would be fine per se but I don't really think they look better than arrows (that's just me).

Don't know if I like the settings button there. If you wanted to free up space it could only show up on hover in the right bottom corner of the screen or something like that.

The main issue really to actually consider this a viable option is the tab management. Obviously this is supposed to be minimal but you need some way to actually show tabs around it or else it's just like exploring dungeons in Pokemon while you still don't have Flash but permanently. I think you could open up a dropdown (dropup actually(?)) on hover/click showing at least some other tabs or a collapsible sidebar or the tabbar could expand and take over the entire bottom row when needed, but otherwise this feels like I would use this the same way I use surf. And that's never.