Now I didn't see the incident and I suspect very few if any of the previous posters on this thread did either but give this some thought as it does not appear to have been mentioned yet.
The a/c was pushed back too far resulting in the main gear (one or both I don't know) ended up leaving the concrete and sitting on the frozen ground. Is the grass lower than the concrete? Is it just because of the "lip" that the tug was unable to extract the a/c from the frozen ground?
Assuming that this may have been the case, the tug would have been spinning its wheels on the concrete because of a lack of traction. One way to assist this would be to apply a little power to both a/c engines (to keep things aligned) and assist the tug. Knowing this may be a bit dangerous, the captain may have decided to get the tug out of the way before trying it.
Many years ago, a tug was struggling to get traction to drag a DC-10 into the hangar at Gatwick so the hangar manager who was trained to taxi, jumped into the left seat, started #2 and used a/c power to drive it into the hangar. Nobody died and sometimes, careful use of the available tools (engines) is all that is needed.