Checkbox in red rectangle is "One response per person", I have exactly unchecked it before I send the survey.
But during my testing, "Submit another response" doesn't appear.
Only thing I can think of that might have gone wrong is that the form didn't save your change after you made it.
If you haven't tried yet, tick One response per person and give it a few seconds to save the change (you'll see it saving in the top of the form where the form name is).
After it's saved, untick the box and wait again until it saves again and then Preview the form and see if that does the trick.