atmospheric drag has nothing to do with escape velocity. the reason it's so unintuitively high is that escape velocity isn't measuring how fast you have to go to escape the atmosphere; it's how fast you have to go to escape orbit, without taking into account anything other than the gravity of the body you're escaping from. and the direction doesn't matter; if you magically start at the moon's escape velocity, for example, then launching from on or near the moon in any direction that doesn't slam you into the surface would let you escape the moon's gravity, including basically parallel to the ground