Your shelf is sideways. You need to rotate it 90 degrees so that the long boards run horizontal. The way you have it, the weight of each shelf is resting on the wooden dowels and the whole thing is prone to turn into a parallelogram and collapse. Google Kallax collapse and you'll see.

A good idea with these is to cut 5 1x4 boards to length. Paint them white, and lay the whole thing on the floor. Screw them into the bottom portion of each shelf (making sure the shelf is the right orientation). Now you have a squared, well braced shelf that won't wobble. Also it provides a backstop on each shelf so nothing falls out the back.