How do I repair improperly backed shower tile?
In those years, wonder board (cement type backer board) was not in general use yet.  Green board was still widely used with a couple of coats of paint over it.  And as you are very well seeing, it did not stand up to moisture for the long haul as was expected.  If the tile sealing was not maintained and or the grout lines, within 5 to 8-years the whole shower was falling apart. 

The gap was intentional. It was meant as an air gap.  Water was not supposed to wick across the gap up into the drywall board and thus last longer. 

No easy answers here.  Recommend you simply tear it all out and start again.  The new cement type backer board is far superior to what you now have. P.