It should be tempered for both....
Playfield
absolutely.
Backglass because it may twist and break when removing or installing for maintenance or even moving of the machine. Standard glass doens't bend much before breaking.
(hmmmm....you said yours was already broke right?)
They should be able to get the exact right thickness you need.
Should actually only be around
3/16", so with the glass and the 1/16" underlay/graphics would be a total of 1/4" + plastic strips.
How wide is your backglass groove?
Anything tempered has to be
ordered in because it can't be cut after it's tempered. The glass has to be manufactured to size and then heat treat it for the tempering process.
the machine does not have tempered right now & the problem is with the tempered it has to be ordered in & there is a 1/16" tolerance, so a 1/16" on 3/8 could make it a little tight
All suggestions of course.... aside from all the safety reasons, but it will pay for itself the first time the regular glass gets broken.