I love the visuals. They gave me that Megaman feeling. It was really nice.
The music is a bit odd... I like how it changes when changing time, but it sounded quite consonant. Maybe trying to establish a stronger sense of rhythm in some parts would help. Also adding some more tonic notes (i.e. the notes the scale is named after). You're leaving the listener hanging a lot of the time, by avoiding them. I think that those two things could make this piece even better. Doesn't mean that they will, it's just that this piece sounds overly aggresive at first.
The idea is simple but I liked how it was implemented. The time grenade was nice, but I had too many of them which made it so I didn't ever want to fight the enemies.
The movement was a tad bit odd. I didn't like the floaty jump. It made the movement feel unresponsive.
I got stuck in the end. You get softlocked if you come to the right of the red capsule enclosed with the pair of red doors if you don't have the keycard. My game crashed after that, so unfortunately I didn't finish the experience, though it was nice.
I'm kinda curious, so I'd like to ask. Why did you choose the name "Red Empire"? The soldiers don't really resemble any redness with their appearance. Maybe it could've been incorporated by adding some red symbolisms in their clothing (show-don't-tell rule).
Good job!