The phrase "absorbed in playing" is correct and usable in written English.
It can be used to describe someone who is deeply engaged or focused on the activity of playing, whether it be a game, a musical instrument, or any other form of play.
Example: "The children were so absorbed in playing that they didn't notice the time passing."
Alternatives: "engrossed in playing" or "immersed in playing".
But once you learn how to play an F chord you become more deeply absorbed in playing the guitar".
Some collected manga books, others got absorbed in playing at being their heroes, and I was excited to draw the characters, because I was good at drawing.
Absorbed in playing with the lightning-fast cyberspace synapses of the global economic body, why would they even bother to look?
Children naturally become so absorbed in play and artistic activities that they lose all track of time.
But stay away from this app if you don't like spending hours deeply absorbed in game playing.
His human subjects -- among them his wife, Anne; his five children; himself; and friends -- are often placed in highly specific settings, like "Laurence at the Piano" (1953), in which his teenage son sits absorbed in his playing before a view of the living room and dining room doorway of the Southampton house.
The aesthetic spectator is swept up by her experience of art, absorbed in its play and potentially transformed by that which spectatorship helps constitute.
Did you ever become so absorbed in your play as a child that you didn't hear your mother's voice calling you in for dinner?
It may also be difficult, if not impossible, to determine whether a player's brain damage was the result of hits to the head absorbed while playing in the N.F.L., in college or at some other time.
He had also become absorbed in music, learning to play five instruments.
But despite some slapdash sentimental subplots -- a busy scientist and father too absorbed in his research to play soccer with his son; Lou's agonizing choice between human companionship and a life of secret-agent adventure -- there is enough dopey, exuberant fun to delight children without driving their parents completely crazy.
