After gambling with the one npc and won, I went back to the other npc who gave the quest, but never got any reward for it, yet it showed the quest as being completed. Would it be possible for me to get the quest rewards?

I think the XP rewards were added much later to these quests - this one has the XP reward added to the FFXIclopedia in 2013. You should have gotten the map though, unless you'd already bought it. Check your key items.

Oh so that’s why I didn’t get anything...I already had the map and the XP rewards were added at a later date