Does introducing an element of play, hunt, or competition make feeding more rewarding?
Yes. See contra-freeloading or (for humans) ikea effect.


  Contrafreeloading: (verb) The behavior in which animals offered the choice between eating food provided to them for free or working to get that food would eat the most food from the source that required effort. This term was created in 1963 by animal psychologist Glen Jensen. Jensen ran a study on 200 male albino rats where the end result was the rats ate more from the food source where the rats had to press on a bar to get the pellet rather than the dish of pellets where they didn’t have to do anything at all. Jensen then studied the behaviors of gerbils, mice, birds, fish, monkeys and chimpanzees. In fact many have studied contrafreeloading since then with similar results, except for the domestic cat – which likes to be served. This 1963 study’s results were surprising because it would be more logical, from an evolutionary point of view, to not expand energy to get food when food is freely available. Why do pet bird people care about this? Birds seem to want to work for food, which is a wild instinctual behavior. Avian behaviorists recommend that pet bird owners encourage contrafreeloading behavior with foraging setups and bird toys within the pet birds’ cages and that pet bird owners engage their parrots by training commands like Step up or tricks such as the eagle, and then use a treat reward system. This keeps pet birds busy, active and healthy.


From http://www.birdchannel.com/bird-words/contrafreeloading.aspx