Tractors are not completely idiot-proof (thankfully). Just because it can doesn't mean you should. There are mechanical stresses which can be induced that were not intended to be be accommodated by the equipment's design. Things will bend and twist if the operator simply fiddles with the controls with no mind toward some basic principles of physics. As merely one example, when he is carrying away the tree, the fact that the rear wheel opposed to the majority of the load is coming off the ground is pretty good indication of a substantial imbalance being placed on the loader frame and associated cylinders.I don't see it as overtaxing his equipment. Granted, he's taking it closer to limits than "normal", but it's not like he's hitting a concrete curb with his bucket at 5mph. Yep, a stick could of went through oil pan, more likely root ball would lift tractor by front axle.
I see the biggest danger in that a widow-maker may come down and crack his skull when shaking the tree, or worse yet, it could dent in his hood. Granted, maybe less likely on a healthy looking conifer tree than a dead hardwood.
He's also lucky that when pushing it away that tree didn't bow then snap back right up the loader arms into his lap before he could stop, or worse yet, rip out a hydraulic line.
Trees are more creative than you are.
That is, they can think of ways to mess you up that you can't even imagine.
If you think you can imagine all the ways it can get you, you're wrong, it can invent a few more.
Get a cable and pull it over from a safe distance. ....of course the cable can snap and kill you, just like a chain saw could if you cut it down. Just like a stump grinder...etc....never mind....do what you want ...it's a free country.
p.s. Yes a rear wheel is off ground, but one can't tell if this is a great imbalance to be concerned about. A nearly balanced lift will typically only lift one tire off the ground because front end pivots.
………………………..I can't believe the comments I'm reading here. Tractors are made to be used. Enough said!