In short, in the video there’s an interviewer who goes to a medium who tells him that his grandmother had very small feet, and he didn’t know that, but he checked with his father and his father confirmed it. Also, she told him that his grandmother had a brother who was murdered, and that detail also turned out to be correct. Another medium took the interviewer back to another incarnation, where he reported that he had been a woman who was executed in Tsarist Russia at age 43, in a basement, shot in the back, and her husband was hanged.

One of the mediums in the video, named Tami Goldstein, appeared on a television program called “The Power” that aired about 14 years ago on Channel 10. There too she demonstrated supernatural abilities, for example: they put a picture in an envelope and she knew who the picture belonged to; they brought a person into a dark room in front of her and she knew who it was; a couple came to her and she was able to say that they were married and that they had had a baby who died; they hid a person in a large forest and she found him; they hid a person inside the trunk of a car in a parking lot full of cars and she found him too. The examples are taken from this video:

I don’t know. You’d have to check the reliability of the videos and make sure there’s no trickery there. Beyond that, there are many unexplained phenomena that don’t necessarily point to reincarnation. There are even mentalist phenomena, like with Lior Suchard, that would look very similar to you. And maybe there is such a thing as reincarnation too. But I’m pretty skeptical, because testimonies like these, when subjected to serious scientific scrutiny, usually fall apart. You can find many such critiques on skeptic websites.
Some of the cases here don’t indicate anything at all. The fact that they brought the interviewer to saying that he was a woman who was shot—what exactly does that prove?

It means that either he’s lying, or imagining it, or reporting something real. He has no motive to lie. As for imagining it, the question is why he would imagine דווקא such a thing out of all the possible things.