If he plays holes 10-18, we would say that he is starting at the 10th hole, or "playing off 10."
Can you provide more context?
Unfortunately there's no more context. Two people are talking about a third person who plays golf. One of them says "He plays off ten" but doesn't even know what that mean!
But thank you very much, your explanation was very clear.
Even though I don't know how to translate it...
Sounds to me like "he" is "her" husband or partner and has possibly been boring her with his golf stories, and my interpretation would be it means his handicap.
That wikipedia page mentions "giocano scratch", so maybe you could translate it simply with "Gioca dieci"?