Can the indefinite article be omitted: 'ο άντρας αυτός είναι παίκτης γκολφ'?
Ο άντρας αυτός είναι παίκτης του γκολφ was marked wrong. Ένας is not needed here as he can't be two golf players
Added! The indefinite article had not been omitted for that word order in the alternative translations.
Are you sure? I just typed "ο άντρας αυτός είναι παίκτης του γκολφ." It was rejected. Is there some other error I have failed to spot?
Yes, I remember changing it, but can't find the sentence on the database any more :/ Your answer is correct.
"αυτός ο άντρας είναι ένας καλός παίκτης" - why not???
The sentence says 'golf player' not 'good player' ;)
And what about the word order in "Ο άντρας αυτός"? Is it completely equivalent to "Αυτός ο άντρας" or it has an extra nuance in meaning?
It is the same thing. In Greek, syntax is very plastic. In this case there is no difference. Generally there is a difference in expression.
How about "παίζων γκολφ" for "golfer"?
Παίζων is an active voice participle and means "the one that plays golf (now or in general)". It does not exactly mean "the golf player". Also, it's a bit archaic.