Sure, he's run for president recently, but Gingrich hasn't held elected office since 1999, when he resigned as Speaker of the House.
But, if you think about it, it makes perfect sense.
See, Gingrich is part of the old Republican party, not this new, more radicalized one. Compared to say, Ted Cruz or Donald Trump, Newt Gingrich is downright progressive.
By picking 1999 politician Newt Gingrich, the Republican party will, in a sense, be moving itself nearly 50 years into the future!
Still not quite the present, but to them ... THE FUTURE!