Do you need to control both battlefield fields to win with Purple Yasuo Wind Rider ability?

No, you do not need to control both battlefields to win using the ability on Yasuo, Windrider.

According to FAQ #8431, the point scored from Yasuo, Windrider's ability is not restricted by the standard scoring limits that apply to "Conquer" or "Hold." Consequently, you can score the winning point using this ability even if you have not conquered every battlefield that turn.