Diane Ackerman defines Deep Play (in her eponymously titled book of the same name) as: 1. A state of unselfconscious engagement with our surroundings; 2. An exalted zone of transcendance over time; 3. A state of optimal creative capacity.
And yes, you could say the same thing about Deep Fun, except fun is not quite the same thing as play. Play is one of the things we do for fun. Fun is what we do because we can.