There could be something to this idea but the implementation is a bit harsh.  In games like this you usually want to favor the player and give them the benefit of the doubt.  For example if you jump through a gate with the right pips showing you can just barely not make it across and then when you jump again you die because you have the wrong pips when your bottom corner is just barely touching the gate.  I would just make it so that when the player passes a gate the gate is destroyed.

I also think that the hurtbox for the player should be slightly smaller than the sprite for the player in most games just to give them a bit of leeway.

I got stuck at level 6 where there's a gate that seems to just change completely randomly with no predictably timed cycle or pattern and no warning to the player.  It could be a six for 5 seconds, then change to a four, so then I try to pass it with a four only for it to instantly switch to a three in an instant.

The game looks great and the physics for the die feels nice.  You should feel proud to make something like this in 48 hours.