The goal frame is not another player
Law 14 prevents the penalty taker from playing the ball again until another player has touched it. A post or crossbar is not a player. That creates a practical difference between two rebounds that may arrive in almost the same place.
Picture a penalty striking the right post and returning straight to the taker. Now imagine the goalkeeper gets a hand to the shot before the ball returns. The taker sees a loose ball in both versions, but the intervening contact history is different.
Replay the rebound backwards
Begin with the follow-up shot, then work back through the path: taker, rebound surface, first shot. A fingertip contact can be difficult to see from the main angle, so a close-up of the save may be more informative than another view of the follow-up finish.
The distinction matters specifically to the original kicker. It is not a blanket rule that nobody can play a ball rebounding from the frame. Nor should this ordinary in-match illustration be transferred to a shoot-out, where there is no continuing open-play follow-up by the taker. Label the phase first, then identify the intervening player contact. That pair of observations resolves much of the confusion around an apparently straightforward rebound goal.
Questions answered
Does hitting the post satisfy the other-player condition?
No. The frame is not another player.
Does this describe open-play follow-ups in a shoot-out?
No. The example is an ordinary penalty during the match.
Sources & further reading
Official references for the subjects discussed. Service terms and device software can change.