No game, as you understand the term Donal, is inferred --the young man has seduced the lass and is pointing out that many another lass has enjoyed the same experience without being found out.
Can remember singing the song in Tarland some forty years back, on the fourth day of a five day wedding celebration, and was somewhat taken aback to find that none of the local people had ever heard of it.
Tarland of course being the locale of the song.