First video is Tai Chi vs BJJ, not Judo. The Tai Chi guy demonstrated some legit skills standing, but he was just outclassed. He got taken down fairly easily, but by someone who was both highly skilled and much younger and more athletic. Once on the ground, he was more out of his element and the BJJ guy could have submitted him easily, but was being friendly and was content to just stay on top.
The second video I think was a bit of a setup by prior arrangement, although you need some experience to see it. The Tai Chi guy had a good base, but no more so than an equivalently skilled Judo practitioner. The Judo player seemed to go for some legitimate throws, but he didn't set them up the way he would in competition. He voluntarily went for a no-gi style clinch rather than taking grips on his opponents uniform as would be normal in Judo competition. He didn't use grip fighting, feints, combinations, or proper kuzushi to setup the opening for a throw the way you have to against an opponent who has a good base and is being completely defensive the way the Tai Chi practitioner was.