Axial means in and out,... along the axis,... but it doesn't matter. 2mm / 0.05mm is 40 times more movement than you're supposed to have.
These are the specs for the speed sensor:
If you've got 2mm of movement,.. you may have moved your sensor clearance way out of spec, so it can't read the wheels rotation.
Generally speaking if you can feel the movement it's time to replace it. (I wait until I feel movement,... 0.05mm is ridiculous tolerance,... same goes for ball joints, tie rod ends, sway bar links.... )
Remember that 2mm gets multiplied further out from the axis,... so where the rubber hits the road you could have 2 or three times more movement. Put your wheel back on and wobble it around and you'll see (with the wheel lifted off the ground),... that will wear out your tires and make it unstable especially on front wheels.
I just noticed the resistance inspection is listed in my post,... you could check that too but I think the connector is buried in the hatch area.
You should just replace the rear hub assembly,.. then worry about the sensor if it doesn't start reading.
Check out this thread,... you may have a seizure to deal with and your bearing might be stuck too,....
http://www.mazdas247.com/forum/showthread.php?123830608-help-seized-wheel-hub-assembly