The steering gear has 2 shafts.
The one attached to the steering column, there is an adjusting nut that adjusts that shaft play.
The other shaft is attached to the steering arm it too has an adjustment and if it is out of adjustment the shaft can move in and out of the gear (ie up and down)
It is really surprising that the gear would be out of adjustment after 15,000 miles, mine went 250,000 before it needed an adjustment.
What evidence do you have that the car only has 15,000 miles?