If the glass is in a slot and the sides were assembled with the glass
in place, there are a couple of possibilities:

(1) Disassemble two corners -- espcially nifty if you can make them
diagonally opposite.

(2) Get someone with a rounter and a small bit that cuts a narrow kerf
and have them set up a straight-edge guide (or use a router table)
to remove the wood on the inside side to the depth of the notch.
This will allow you to remove the old glass. You can then install
the new glass and add standard glass retainer clips with short (1/2")
sheet-metal screws (probably #6 diameter) to keep the new glass in
place, which is what should have been done when the door was made in
the first place.

Clarke