Do cards like Kai'Sa or Qiyana that trigger on scoring/conquering work if you win combat at 7 points (where you don't gain a point)?

Ruling: Yes, you still score (conquer) the battlefield even at 7 points; you just draw a card instead of gaining the final point. Cards that trigger on scoring/conquering will still activate.

Sequence:

• Win combat on a battlefield you haven't scored this turn
• You score (conquer) the battlefield
• Instead of gaining the 8th point, you draw a card
• Cards that trigger on scoring/conquering activate

Nuances:

• You must not have already scored that specific battlefield this turn for the scoring to occur
• At 7 points, if you would score on multiple battlefields, you draw a card for each instead of gaining points