Wikipedia’s definition of an open border is “a border that enables free movement of people between different jurisdictions with limited or no restrictions to movement.”
Since Newt believes in securing the border, he doesn’t fit the definition of an open border Republican.
Newt also is opposed to a border fence. Which means his talk of securing the borders is just lip service.
Check out sites like numbersusa.com and fairus.org for border security info (factual info with plenty of supporting data).