The epitome of awesomeness
First let me say that the people who whine about it being impossible, or say the controls suck, those people are just too stupid to understand basic physics. The gun, it exerts a force. That force is slightly less than the guy's weight. It can oppose his downward acceleration. It cannot make it positive in the upward direction. Thus it cannot lift him off the ground, but it can all but halt his downward acceleration, and maintain the upward velocity he gets from jumping for a long time, all that while his upward position will just keep going up. So if you fire down as you fall off a ledge, you will note that you accelerate down slowly. And the way to jump high is -any reasonable intelligent being will be able to tell you- to jump and immediately start firing straight down. Seriously, it's so obvious!
There are a number of things about this that I REALLY like:
1. First of all, I love the choice of music. I heard that exact same music in another game I played, and that game was awful - but it fits this perfectly. Its upbeat-ness is mixed with chaos and therefore sardonic - which fits the scenario exactly.
2. Another thing, this is THE SCARIEST ALIEN INVASION EVER. EEVVEERRR!!!! I mean, look at the friggin' background for crying out loud, with the ships all over the place, sending the giant crabs down, while the giant claw drags the guy's future self away! The shock value to that scenario is like nothing else imaginable! Yet the guy calmly follows his future self, knowing it will soon be him who is being mutilated. I especially liked the ship in the background right before you get to the boss, that makes that HUGE blast in the landscape that puts an H-bomb to shame.
3. The ending is different from the beginning. Obviously deliberate since that means the artist had to animate it two distinct times instead of reuse the animation he already had for the first one. The guy doesn't have the sunglasses and the red shirt, he's dressed exactly the same as his earlier version this time. The claw is also different. But that's not as interesting as the time travel ontological paradox surrounding the gun. Where did the gun come from? The past version got it from the future version, and he loses it to his past version when he becomes the future version. So it's not an alien technology, it's an artifact of the time travel, that came from nowhere, and potentially is infinitely old as it has been through the time loop an infinite number of times. Infinite energy reserves. A very special gun indeed. I want that gun. That gun is awesome. But alas, it is conscripted to remain within the time loop and exist nowhen else.
4. The easter egg is awesome. Nice use of the doc brown quote. Although an error really made me laugh: an error in the animation that comes with it. When the guy goes back to the past, his earlier self, who also has the dinosaur head since he has apparently changed all history, look at his clenched teeth while he's grimacing! They're in a mouth in the middle of his neck! The author interlaced the original image and mapped it wrong to the dinosaur head! It should be the mouth on the dinosaur head grimacing.
5. The guy's comments, while he's being mutilated. Just great for increasing the shock value, yet your character calmly and obligingly follows the floating claw. Awesomeness.
It's a worthy alien invasion. I have always looked down on hollywood movies where they propose that we would be in any situation other than hopelessly outclassed in the event of an actual alien invasion, but this tells it like it is.
The people who give out science fiction awards really should re-evaluate the times they live in, and start giving awards for video games. After all, there's a Hugo award for dramatic presentation, and 100 years ago movies were a new thing too, so there was a time when that novel medium became acknowledged. It's time to do the same here. I would certainly nominate this to win such an award. I hope you redo it with a longer and more detailed story (but the same music, because that music's really great for his concept).