You don't "need" to be able to stick a
grapple underneath something but it is an advantage. It allows you to exert force upwards by driving the tractor after inserting the
grapple underneath. Of course you can also just put the
grapple against something (rather than underneath) and pushing. The standard
grapple allows you to do both, the claw only allows the pushing. I often find with a tree that is a little too big to easily push over that I can loosen it by alternately going underneath and then pushing when pushing alone doesn't work.
The video you posted didn't seem to show much more than just collecting very small trees and forest floor debris. Either style
grapple would work for that task but the claw type is more expensive and heavier. He wasn't pushing over bigger trees but he could have with a tracked skidsteer. A CUT will have trouble pushing over trees that a skidsteer can easily bulldozer over. The way to do it with a CUT is to undermine the roots with the
grapple and push from different sides. It will take longer with a CUT but it is not a function of the
grapple it is related to the advantage a tracked large skidsteer has over a CUT.
I did note that on the skidsteer video they have a type of claw that is kind of a hybrid. The upper jaw is not a true claw jaw but more what you would see on a standard
grapple. That is obviously to allow a larger load and to avoid the pinch phenomenon that I described earlier where one big log will prevent you from loading other smaller stuff.
The
grapple in the video is probably 72# and weighs about 1200-1500lbs and costs about $3000. Those are really designed for skidsteers and excel doing small debris pickup like the guy in the video is doing. I can do the same work with my 48" standard
grapple though so I don't see any advantage for a guy with a CUT. His $60000 skidsteer
grapple combo would presumably be faster but I can get the ground looking just as clean as he can.