I almost made a very similar game, but I changed my mind about time traveling midway through, with the main reason being it felt kinda pointless going backwards in a racing game, and I think it kind of applies here, the optimal way to play is to not use the rewind, right?

I really missed a brake button though, especially near the end where the curves come out of nowhere because of all the twists in the track. My shots would always miss as well, since it would always shoot at an upward or downward angle.

And I was very surprised to see the game has no keyboard controls, even though I had already pulled out my controller before even trying. You can always put a "Controller preferred" sign somewhere but to take away completely the possibility of playing with keyboard is, at the very least a bit curious, considering the inputs involved. Does it rely that heavily on analog controls? I couldn't notice, and considering the racing game I'm most familiar with is CTR played on a d-pad, I don't think I would anyways. 

Do I have to use a controller?  I cannot click on anything in the main menu.

Great idea. AI is hard and  faster than I can line the car up and use the rewind beam on them. Cool style for the visuals.

I got stuck on main menu. I have tried clicking every button on my keyboard and nothing happened :(