Good American fan of Grand Theft Auto? (5)

I believe the answer is:

gamer

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'good american fan of grand theft auto?' is the definition.
I can't judge whether this definition defines the answer.

'good american' is the wordplay.
'good' becomes 'g' (abbreviation).
'american' becomes 'amer' (rare abbreviation).
'g'+'amer'='GAMER'

Can you help me to learn more?

(Other definitions for gamer that I've seen before include "One having fun with computer" , "I bet" , "More handicapped" , "Keen computer player" , "One role-playing on computer" .)

I've seen this clue in The Times.

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