Take the wire on the right hand side. It experiences a force to the left of the page. To experience a force pointing left-wards, the magnetic field must point into the page. Why does it point into the page, given that magnetic field tangents run in all directions from the circular field?? If we identified exclusively one direction of travel, B could point rightwards as much as it does point into the page.
I understand the right hand rule used to determine the direction (clockwise or cccw) of the magnetic field around a current-carrying wire. In the given diagram, the field lines run counterclockwise, but I can't identify a justification for choosing a field line that points into the page.