I will answer the easy question first: Yes, it should really be "The point being..." But sometimes when people are speaking informally, they drop "unimportant" words, and it's somewhat idiomatic to just say "Point being" instead of "The point being".
The point being is an example of an absolute construction, using a present participle. An absolute construction works kind of like an adjective to another phrase, and describes something about it, like the cause or the setting. In this case, it's sort of like saying "Because this is my point:".
You could use it like
The light fading, we hurried to set up our tent.
where the light fading describes the situation and the reason we hurried.
My horse having died, I was on foot.
where my horse having died could be rephrased as "Because my horse had died".
Another good page on absolute constructions: https://www.thoughtco.com/absolute-phrase-grammar-1689049