Bravo for Mike in rush for game (8)
I believe the answer is:
scrabble
'game' is the definition.
(Scrabble is a board game)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for scrabble that I've seen before include "Disorderly struggle" , "Popular board word-game" , "Scratch or grope around" , "Board game with letters" , "Struggle to gain possession" .)