An interesting story, but I wasn't able to make it all the way through. There's a bit too much dialogue for the action game you've set up here. It took way too long to get into the game, and every sequence being interrupted with more story really detracts from the experience. Though, I was curious to see where it would go.
I would suggest maybe working the dialogue into the action somehow. Like thought bubbles around the player or something like that. In addition, the mechanics and gimmicks of the levels were introduced a bit too slow I think. It felt very same-y for the first two descents after my weapons were activated. Could have used more variety to keep the player from getting bored (and then turned off by the next dialogue sequence).
I think this has some potential but will need some design reworks to improve player retention.