Good effort, but to my mind fatally flawed.
Currently, if you change direction, you have the character walk a small semicircle before heading in the direction you press. When I say 'small', of course, the total size of the circle seems to be about the size of one of your platforms, so relative to the game, the character is actually meandering quite a distance.
The end of effect of this is, if you are facing west, and you press to move east, the character turn to face south *while walking* and end up moving east along a line parallel to your former westerly path, but further south. If you are trying to jump along a set of platforms that are aligned east to west, and you only press the east and west direction buttons, you will keep falling off the north and south edges of the platforms, which is absurd and frustrating.
But even worse, because you have the character always walk in the direction its facing, even when turning to face another direction, if you are facing west and move to turn east, you *start by walking west*. I understand you want to have the character move in a realistic way, but A) this isn't realistic and B) it ruins the platforming.
It is somehow worse than the old fashioned tank-controls, because you have all the flaws of tank controls, while not actually being able to turn in place, like a tank does.
Aside from the terrible controls, I also have a few minor nitpicks:
Why do you have mouse controls, if you aren't using the mouse itself in the 3-D environment? It's nice to have your hand on WASD and your hand on the mouse, but if you are only using the mouse for buttons, it seems like it may as well be a keyboard only game.
I appreciate that you want to use the white objects and white background to make puzzles, but while using angles to hide objects can make for interesting hide-and-seek problems, once you have found an object you never really locate it well enough to do things like judge distance, either. Considering that platforming in 3D is already very hard because of perspective problems, removing information is only making it less fun.