that looks like it protects everything except the bits that will hit the ground
I have a screen protector on my 8+ but no case.
I hate cases on phones. I have never used 'cases' except for a light blue rubber 'bumper' for my 4S. I could still appreciate the glass and design whilst having some rubber protection on the edges.
I wish Apple did something similar for the 8+ but most of the cases have backs. The 8+ is very slippery though so I am swaying towards getting a case but haven't decided yet.