Electrons have mass, and therefore momentum. As long as they are fast enough, they are not likely to change their direction much. Also, when leaving the cathode, the anode is far enough away, so they are pulled towards the center of the ring anode (because the anode is symmetrical) and are barely accelerated towards the ring itself.
Most important: the electrical field in the plane of the cathode ring is almost zero, so there is barely any force on the electrons towards the ring. Furthermore, the inverse-square law applies to point sources of an electrical field, the field in a different geometry can differ significantly - like between charged plates, around a charged rod, between two point sources of opposite charge or inside of a charged ring. After all, nobody says that none of the electrons hit the anode. Some certainly will and if you measure the current required to sustain the high voltage, you will see some leakage current, which comes from those electrons hitting the anode.