If I conquer a battlefield on my turn, my opponent conquers it on their turn, then I reconquer it on the same turn (opponent's turn) by killing their unit with Ride the Wind, do I get a conquer point?

Ruling: Yes, you get a conquer point and the card draw. You can only score 1 point per battlefield per turn, so if you already scored at that battlefield during your own turn, you cannot score there again until the next turn cycle.

Nuances:

• If this would be the final point of the game, you cannot score it unless you have scored at every battlefield "this" turn. In that case, you would draw 1 extra card instead of getting the final point.
• Other cards may override the one-point-per-battlefield-per-turn rule if they explicitly say otherwise.