Nice prototype! The character is quite well-modeled and animated. Transitions between the "pushing" hint vs. other walking is a bit abrupt, though, but it works and makes sense. Also kudos to the outlining of active buttons/etc.
Like others, I'm not a fan of top-down plus direction-specific WSAD movement. Took a bit of time to stop falling off the edges accidentally. :) But, thanks for bringing us back to the nearest box spawner. Perhaps don't allow the player to fall at all?
If you keep WSAD being player-direction specific, maybe it would be better to force movement to the nearest 45 degree angle? A lot of my time was spent nudging boxes into the proper direction so they wouldn't go at strange angles.
(An alternative is to just turn the world so it's always "in front" of the player. That could solve both control issues, assuming these are real 3D worlds and not clever 2D maps. But I understand that's a big look-and-feel change.)
Hope it wasn't just me, but I didn't hear any audio. Sound effects would help a lot too to provide feedback.
Another minor issue is that sometimes, walking near an open bridge shows the closed bridge for a frame. Nothing breaking, though.
Looking forward to more!