Slightly amazed by how swiftly by how quickly Daphne took off, Apollo gave chase at a more leisurely pace than Ate. He assumed that the Goddess of Ruin would route the nymph between them so they could effectively trap her, and he was fine with that plan.
He could move faster, however part of him wanted to see the hope in Daphne's eyes when she thought she truly stood a chance of getting away from them. He knew that it might be rude to play with one's food, however she made it so damn fun!
Flashing an amused smirk to Ate he could see that she was enjoying herself. They would most likely be celebrating later, and he knew it would be quite fantastic.