The gap is that it did not specifically define what “natural born citizen” actually is.
Defining “citizen at birth” doesn’t help to define “natural born citizen”.
The only gap to be found is in our knowledge, not in the Constitution. The term had a definition in 1787, and the framers understood it. (Otherwise we’ve got them writing nonsense.)
We’d be better off hunting down their definition than trying to shoehorn ours into the document they wrote and ratified.