If your dog doesn’t want to participate in a certain game or work on a food puzzle, it’s probably too hard for them. You haven’t made it clear enough how to win the game. Go back and make it easier, and progress more slowly to greater difficulty. Often dogs need just a bit of encouragement and to be shown that success is possible.
A dog that wanders away and can’t be bothered to participate at all is very likely confused. He might also be bored, not hungry, or not enticed by whatever food is on offer. If you’re offering an easy puzzle with something really good inside—say it’s a Kong filled with mash sardines—and your dog just shrugs and wanders off, that’s fine. Scavengers, opportunists and feral dogs sometimes go for a day without a meal, fasting. If your dog is a healthy weight, has a good bill of health from a recent vet check, and only occasionally decides they want to skip dinner, it’s no big deal.