A very small amount of play on the 'Z' axis, (up and down) won't hurt anything as long as the 'rod of death' has clearance to be manipulated when necessary and it's achieving positive lock up in it's hole.
Front to back movement can be very bad. That backplate takes the full brunt of the bolt's violent rearward travel every time the gun is fired. The impact is considerable.
Slop can lead to failure of the milled slots eventually. (back of the receiver cracking off.)
The force the the recoil rod holding the plate back is insufficient to prevent eventual damage. You want a snug, solid fit.
The idea is to keep the backplate firmly against the slots, pushing towards the rear of the gun. NO forward movement. No sense giving it a running start, right?
Easily fixed though.
First, try swapping you dad in law's backplate in there. If it fits snug, STEAL IT!!

Yup. Bad joke there. Don't do that.
All you need is to eliminate any front to back movement. You want the backplate held firmly against the REAR of the slots in the side plates.
Quick and simple fix;
Pull the backplate. Carefully remove the bolt, keeping the recoil guide rod pointed away from people and set it on a shelf with the rod pointed towards a wall or something else solid but cheap to replace.
The idea is to build up thickness of the tongues on the Front Edges of the tongues. This will force the backplate tightly to the rear of the slots where it belongs.
Using a ball peen hammer, very lightly strike the front corner edge of the bottom right of the tongue about one inch up from the bottom. You're pushing a tiny bit of metal forward on that corner.
This will raise a tiny bump on the forward facing edge of that corner.
Slide it into the gun and check for fit. Wiggle it around to see where it needs more attention.
Too much? One swipe at a time with a small diamond file or tiny sanding block, then check again.
Not enough? Peen it a tiny bit harder.
Do the same for the forward tongue edge on the left side .
Then do likewise for the upper left and right edges.
DON'T try peening all four corners at one time without checking, assuming the gun and any damage to be fixed will be square and uniform. Murphy don't like that and will probably crap in your lunch box when you're not looking.
Just go one step at a time.
OR just get another backplate and don't get carried away with the media blaster.:tongue: