How did the angel of the LORD depart from Manoah and his wife?

Answer: He rose in the altar's flame

As the flame went up from the altar toward the sky, the angel of the LORD ascended in it, and Manoah and his wife fell facedown.

“When the flame went up from the altar to the sky, the angel of the LORD ascended in the flame. When Manoah and his wife saw this, they fell facedown to the ground.”— Judges 13:20 (BSB)