The one thing one can tell for certain is that the pilot most definitely lost directional control of the aircraft not long into the takeoff roll.  When that happens, a pilot has a decision to make-do I have enough airspeed to get into the air before I run off the runway?, or do I cut throttle and full brakes immediately?  He tried to get into the air, and it sure as hell didn't work... that looked nasty.  I hope the people were ok

That was horrible to watch, but it's always a valuable learning experience...
My immediate impression is that it was probably not overweight, and I don't think he was veering to avoid the people near the strip.  The density altitude there at that moment may have been quite high; it's amazing some times how much that can affect performance... might be a factor.
It looks like he was attempting a normal soft-field (in this case, rough-field) takeoff, which involves geting the plane airborne well below Vx, so as to minimize the takeoff roll on a rough or drag-inducing surface.
The next step after rotation is to immediately reduce the back pressure so the nose can come down and airspeed can increase, leading to a good airspeed for positive rate of climb.
I think what happened is that he gets the plane airborne at a very low airspeed, practically in a stall right away, and at this low airspeed and high power setting, the plane naturally wants to yaw left- which it does, with a vengeance.  He either does not or cannot apply enough right rudder to counteract this (can't see it in this clip), and now the plane is forward-slipping at a very high A of A and very low airspeed. I'll bet the stall horn was going, if the plane was so equipped. Due to obstacles and people ahead, he was probably reluctant to let the nose drop when he should have. 
Meanwhile, there appears to be a bit of a left crosswind (based on the eventual drifting of the dust generated by the plane's passage); this didn't help matters.
What happens next is unclear, because the plane moves far away from the camera, but it would not surprise me to hear he tried to retract the flaps early. He's nearly level, then suddenly the plane just sinks. That's exactly what would happen if you retract the flaps too early, especially at or near gross in a high density-altitude situation.
It should also be noted that it was probably a lot easier to get into that strip by himself than it would be to get out with passengers and medical cargo.... I don't know if he started his roll at the extreme end of the clearing, but every available inch would be absolutely necessary to pull that off...
On the basis of this footage alone, I think his fine intentions (his eagerness to get this kid help quickly, and his willingness to carry the child's very worried mother along when every pound was critical) became a distraction.
Very sad, but a heroic effort, so I'm reluctant to second-guess this pilot... but it just looks ill-planned.

It started out looking like a good, text-book, soft-field takeoff. I think the crosswind was pretty significant because he started drift drastically to the right. I think the combination of the substantial right rudder you need right at lift off during these kind of take-offs.. combined with the crosswind doomed that flight. You not only let up on the back pressure, but, depending on trim/weight/CG.. you actuall fly nose down a degree or two while in ground effect until you can climb out of ground effect with the nose level.  You lose a good 20% of your lift as you leave ground effect. If you try to climb out of ground effect before you're well over Vx.. you're coming back down,, with momentun.

We gotta second guess the pilot here.. or the discussion loses out. And if we learn from it, I'm sure he'd appreciate it.

A near gross-weight, soft-field takeoff into a significant crosswind with possible denisty altitude complications.

That's my guess.

I think Rotty and Brett have it here, the combination of not bringing the nose back down after initial lift-off during a soft/short field takeoff can be very dangerous, as well as leaving ground effect before there was sufficient lift and forward speed.  However, one thing I noticed is that he appears to have at least 20 degrees of flaps, but I always learned that for a short/soft field takeoff, you should only have 10 degrees of flaps.  It almost seems that having that amount of flaps for a high altitude, short/soft field takeoff would hurt more than it would help as your angle of attack would be increased alot, maybe past the point of stall.  Think of when you are landing and you are a little high on approach, you drop another notch of flaps, which allows you to increase your descent angle, without increasing your airspeed (which is the definition of the purpose of flaps).  So I think it is mostly pilot error, the airplane seemed to be doing everything correctly, and the weather wasn't bad (if you look at the trees and other things, it doesn't seem too windy) and the aircraft was just overloaded, and it wasn't able to maintain the climb once out of ground effect.

What T**t. enought said.

But seriously those blokes in front lost their macho persona pretty quick as most people would in that sitaution

Good point, I would have been outta there in a shot