Great concept of linking time to goals, as it adds loads of tension right from the get go.
I also ran into the bug where I would quickly die; like your comment below I feel like that was from the upgrade inventory button becoming focused causing spacebar presses to re-trigger it.
The text wall at the start was also A LOT. I feel like the concept and mechanics can be explained in a few words, really. So making that first entry point feel less overwhelming would go a long way.
I could definitely see this concept expanding into other formats; from 3D shooters like Ultrakill or vampire-survivor style games. This format is also fun, and feels well suited to a minigame :)