I don't have much to add; this is fantastic. It's both a cool sci-fi shooter and cool meta-speculative fiction.
I think the targeting square covers just a little bit too much of the view in front; I had a bit of trouble seeing past it. The four lines by themselves would probably suffice.
While I do appreciate the detail that pressing and unpressing the shoot button fires a shot, I feel like a held shoot control would be more comfortable in this, especially during that final boss!
Great work!