This is not about horses in general or horses in sport. This is about military power. That the king is not allowed to have many horses is to prevent him from putting his trust in military power. Horses and chariots were the tanks of that time. Pharaoh had such a force, but the Lord drowned him in the sea (Exodus 14:26–31). So this verdict to acquire many horses is to prevent the king from trusting in that power.
16 Mais qu'il n'ait pas un grand nombre de chevaux; qu'il ne ramène pas le peuple en Egypte pour avoir beaucoup de chevaux; car l'Eternel vous a dit: Vous ne retournerez plus par ce chemin-là.