Is it permissible to eat birds or gazelles that have been hunted and killed by means other than the Islamic method of slaughter?

Hunting with a trained dog and a rifle is permissible, based on Allah's saying: "And what you have taught of hunting animals as trainers."

For hunting with a dog, it is stipulated that the dog must be trained, it must not eat from its prey, and Allah's name must be mentioned when sending it forth.

For hunting with a rifle, it is stipulated that Allah's name be mentioned when firing the arrow, and the game is permissible even if found dead, as long as it did not have a stable life that would require ritual slaughter (tadhkiyah).

If the game is alive with a stable life, it is obligatory to ritually slaughter it and mention Allah's name at the time of slaughter, otherwise, it becomes forbidden.