Do Big cats such as lions and tigers play with their food like domestic cats do

Lions don't have time to play with their food. Often there is not enough to feed the entire pride, and the cubs will even starve to death. They may fight over food but they don't have the luxury of playing with their food. Besides, hyenas may be lurking and they may try to steal the food if they outnumber the lions. Even in multiple house cat households, the cats may fight over food. Sometimes an adult cat may bring back a live animal for the kittens or cubs to learn how to kill, but the adults don't play with food.

River otters and dolphins may play with their food, but cats in the wild rarely have the time to do so.

Ya they can also play when, if they are not hungry and they have there food. They also use to trained their kids by that food.

I don't think a lioness is going to play with a little field mouse...