Policies at colleges do vary… however, there are enough colleges where enrolling in college after leaving high school disqualifies the student from applying or entering as frosh, so the typical gap year scenario where the student does not yet know which college they will attend after the gap year means being cautious about inadvertently disqualifying themselves from frosh entry at potential colleges.
In this case, unlike typical gap year scenarios mentioned on these forums, college X is the known destination, so college X’s specific policies can be found and followed for this case.