Without cheating and using my limited perspective:
It's most likely Hinduism, with a sort of Brahmanist focus that believes in the Atman or soul, and the self.
Or Eckankar, a religion that focuses on the fact we are a spiritual being living out a physical existence for whatever reason, and Astral
Projection.
Or third guess: various New Age Philosophies.
If you like this, I would suggest looking into Buddhism - it is be an alternative to either, less metaphysics, more understanding.
edit: What I think about it? Sort of self-repetitive. We come all the way down here to astral project? We go through all of this to understand
ourself? We wouldn't have to astral project if we were already spirits. I think we are here because of a million of various factors coming
together, and you can't pin it down to one reason, or purpose.
I remember those videos (or at least the first part) being somehow linked to Osho, that would make sense, since it has over 1.5 mil views and Osho had
a huge following, mainly because his "teachings" (or ideas) were so easily understandable, he looked like a guru, had an amazing charisma and was
funny as #. It's pretty light stuff, and good at that.
That "from the source to the fetus" theory reminds me strongly of the Buddhist 49 days belief. Or rather, like the Bardos, they are probably
originally based on personal experiences achieved by the monks by unknown methods (probably NDEs).
So it could be either, Hinduism or Buddhism. Or a mixture of those. Osho was influenced by both.