Doing touch and goes, the usual practice is to first get it rolling properly down the centerline. Usually the stude will be managing the rollout while the instructor gets the flaps ready for takeoff. Only then is it time to add power.
So here we have power applied when the aircraft is at flying speed which promptly gets it back in the air but seriously yawed
We see an initial right bank to regain the runway, but it looks like a building is in the way; so they continue back left between the building and the woods; then seem to decide to do a mini circuit and head back to the trees.
Had the power been pulled off immediately they got pointed away from the runway, likely they could have got it on the ground and stopped before hitting the trees. Metal would likely have been bent, but survival odds would have been much better.
Some WWII fighters would promptly roll themselves into a ball if full power was applied at that point in the flight.
One question that needs answering is whether the aircraft has enough rudder to keep it straight when full power is applied in such conditions -- or whether it was applied after the swing had already happened.