OP:
Referring to the pic above:
WHICH MOUSE BUTTON are you clicking that is bringing up that "contextual menu"
????
Normally, that's what you SHOULD see when you RIGHT-click.
But... if you're seeing it when you LEFT-click, I think your mouse settings may have gotten mixed up. You have to go to the "mouse" or "trackpad" preference pane and check them.
The next time you see that on your display, choose "open link in new window".
What happens?