A tire machine won't have the pushing power, the wheels would spin easier, ott tracks would help a lot though. That is also a large frame track loader.
They have chosen ideal soil, sand with no rocks to demonstrate the attachment, in the heavy clays and stony gravel we have around here you would have a tough time getting that in the ground the way they show it being done. You would be much better off to weaken the roots with a attachment like that, then push the tree down using the trunk and a bucket full of dirt, then cut it off the stump once its up rooted.
A backhoe attachment (or excavator) would make a much better stumping tool. But of couse the price is higher too,
In tougher soils I can dig a 10 to 12 inch stump out just as fast or faster, in our tougher soil. With a lot less ground distubance around the stump site.
Ken