The rings are there because the maxima from each crystal are at the same angle to the incident beam, whichever way the crystals are orientated. This is the same argument that applies to the formation of a rainbow - same angle gives the appearance of a circle.
This argument is a bit over-simplified because the crystalites can be in any orientation but, as the fringes on a flat screen are equally spaced near the axis, the different orders will still coincide to give rings - but only over a limited range of angles. Off axis, the fringes will not reinforce and the pattern will degrade.