。
I'm too busy to have time to play.
Literal
Busy-[て] play time [subject-が] doesn't-exist.
~くて on an i-adjective functions as a causal te-form: 'being busy, so...' The pattern [verb dictionary form] + 暇がない means 'have no time to [verb].' ひま is the hiragana spelling of 暇 (free time/leisure). がない states that such time does not exist. Very natural casual complaint.