Good spotting.. I think you're right!
Here's the updated shader:
Studiopolis.zip
you simply need to put the glass image in the "texture" parameter of the shader (edit button)
the window object graphic wont' be used at all, only the texture will be used
example:
studiopolis.mfa
(perhaps there's also some y parallax in Sonic?)
for the parallax code see the example,
but you may need to customize it basing on your game,
in short you need to input a floating point value in the ox (and if you need oy) parameter of the shaders,
(as well as coefficients or the thing won't scroll

)
while this parameter grows the texture scrolls
in the example I've taken the player position relative to the left and right screen borders,
but since you will have scrolling, you'll have to take some other "fixed" references inside your frame
try experimenting, I'm sure you'll get to a result!