Am I understanding this correctly—that this is a spaceship that moves across the Life grid by building a copy of itself and then destroying the old one?
I believe so - it's referred to as "Gemini" at the end of the video and it matches up with my (rather handwavy) understanding from reading the forum posts.
I love this kind of in-depth esoteric technical discourse even when as here I have only the most superficial understanding of what they're discussing!