Having rushed for half the game, seemed out of breath (6)
I believe the answer is:
gasped
'half the game seemed out of breath' is the definition.
I can't judge whether this defines the answer.
'having rushed' is the wordplay.
'having' becomes 'ga' (I can't justify this - if you can you should give a lot more credence to this answer).
'rushed' becomes 'sped' ('speed' can be a synonym of 'rush').
'ga'+'sped'='GASPED'
'for' acts as a link.
Can you help me to learn more?
(Other definitions for gasped that I've seen before include "Struggled for breath" , "Breathed noisily" , "Drew breath in sharply as in astonishment" , "Breathed laboriously" , "'Panted, puffed (6)'" .)