Thank you for your feed back ! Yes the title is absolutely a reference to Stephen's Sausage Roll, the greatest puzzle game ever !
For the unintuitive physics i know it can be disturbing early on but the rules are actually simple. Any cube can be the origin of the rotation but the cube being the root of the movement has to be grounded for it to be valid. in this case the furthest block in the direction of you input is not grounded thus not being a valid candidate to initiate the move. The reason you cant go left here is actually the same, the left cube is not grounded anymore.