play, take pleasure in, trifle with, make sport of
玩 centers on engaging with something for enjoyment or amusement: playing, taking pleasure in an activity, or treating something lightly as a toy or sport.
玩 combines 王 (jade) with 元, which likely contributes the sound. The idea is of handling a precious jade object for enjoyment, hence playing or taking pleasure in something.
The left side 王 (jade) suggests a precious toy, and the right side 元 (origin) hints at the source of fun. Picture a child playing with a jade trinket, taking pleasure in its smooth feel.
For ガン, imagine a gun-shaped toy that you play with: gun -> ガン, and you take pleasure in the sport of shooting targets.
toy
caring for (esp. a pet or a small object); cherishing; being fond of; prizing; treasuring
sex toy
pet (animal)
prized or treasured object
pet dog; non-sporting dog
educational toy
The Japan International Doll and Toy Research Association
reading carefully with appreciation
toy
toy shop; toy store
food sold with a toy
toy gun
tasting; relishing; savouring; savoring
toying with; playing with
toy
plaything; toy
toy; plaything
forgetting one's serious objectives by becoming engrossed in trivial pursuits; being distracted by trivial objects and losing sight of one's original goal
food sold with a toy