Unless you're doing a soft field takeoff, which isn't appropriate for the conditions.
Yes, he rotated too early and got himself behind the power curve out of ground effect. That was his primary error. Nothing to do with DA.
Winds can change the equation quite a lot, but with that runway at that altitude, a normal takeoff would have served him much better than that mess. Short field is not necessary. It's 3500 feet to the trees, and they are only 41 feet high.