In my opinion CXW made him push into his strongest structure ( not that this is an easy feat against such a strong power) and the strongman didn't attempt to push upwards. If the strongman had handled a dead body like a fridge, he would probably automatically have thought of this and succeeded.
(trying to connect this explicitly to aikido training)
Tohei would hold against any push successfully and say it was ki training for aikido training.
Tohei would say he was simply extending ki and mention his rules for doing this.
Still, even a strong man like Tohei, with as much strength in one arm like some others in two, in an attempt to show the audience the working of ki, once, was simply tipped over onto his back like a fridge. His partner didn't play the game as expected.
Tohei is said to have successfully influenced the great Chiyonofuji and an other sumotori. So even they must have thought his training method was good.