If I conquer one battlefield but an opponent controls the other while I am at 7 points, do I get to draw a card?

To answer your question: Yes, you draw a card.

According to Rule 448.1.b.2:

"If the player has Scored through a Conquer and has not Scored every Battlefield this turn, that player draws a card."

Explanation:

• The Condition: To earn your final point (the 8th point) through a Conquer action, you must have scored every battlefield in play during that same turn.
• The Scenario: Since you are at 7 points and only conquer one battlefield while your opponent controls the other, you have not scored both battlefields this turn.
• The Result: Because you failed to meet the requirement to score all battlefields, the game replaces the point gain with a card draw.

Important Note: This rule applies specifically to the Conquer action. If you had instead scored that final point by Holding a battlefield at the start of your turn, you would have won the game immediately, as holding does not have the "score all battlefields" restriction.