I don't need to stand by the rotation theory. However, the 2.5 degrees that the Earth rotates are about equivalent to the downrange distance.
The first stage is going about 1/5 of the target LEO orbital velocity at separation. While you might well model the trajectory as a parabola over flat ground, given the lack of fuel I would expect that SpaceX puts a lot more care into their trajectory. So far I've failed to attract the attention of the person responsible for Flight Club, the most trusted modeling of SpaceX flights, but I'll message him directly.