Asking if we play a hand in who we are depends on first answering the question of who we are.

Take the first moment, the very moment "we" come into being: if we do play a role in who we are, did we preexist our self? Or does our self come into being first, and only then do we begin to play a role in who we are? But if determinism is true, and we don't determine that first instance of our self coming into being, then it doesn't really matter if we play a hand in the later sequences, since all the later sequences are now determined.

So, if we do have any kind of self, then, as a determinist, I have to say that we don't play a role in who we are in any sense that really matters.

The other option if that our sense of self, just like our sense of free will, is an illusion. This idea has an ancient pedigree. Buddhists for instance say we've no self! It's the famous anatta doctrine.

I think you're very right to draw a distinction between determinism and destiny as you do in your vid, but I don't know if the "one cause vs multiple causes" is the right way of going about it. Destiny basically implies some mystical force destining you to something, whereas determinism is just science. Determinism would say that if you hit a billiard ball with x force, at angle y, etc., the billiard ball will move in predictable ways. Destiny, on the other hand, says that no matter how you hit that ball, it will move in whatever way it was fated to move.

Regarding the 'multifaceted' point, I think what you're getting at is, to put it pictorially, there's a causal arrow on the left side of a black box, then there's the black box (say that box is us), and then there's an arrow (outcome) on the right side of the box. You're saying that, in a sense, we play a role, because no black box is going to react the same as any other black box. So regarding that, I'd like to point out that that's true of any box, and the box doesn't need to be a human. I.e. it can, again, be a billiard ball: obviously, the billiard ball is going to react differently to a golf ball. What that means is that whatever we grant humans (say agency, or free will), based on that argument, we'd have to grant inanimate objects as well.