Unless there's etching or complicated beveling, it's almost certainly not worth your while to try to "remove" the scratch. Glass is cheap and almost always very easy to replace.
There is complicated beveling, and it would not be easy to replace. The cabinet door would have to be replaced as the glass is very integrally sandwiched into a very seriously glued-together wooden frame.
I think I can live with the scratch, and was wondering if something like Carnauba car wax might make it less noticeable. As you can see from the picture, it is not a traumatizing defect.
The other picture shows the whole cabinet. To get an idea of the scale, that refrigerator is 68" tall. And Bitt, you will be pleased to see that I did indeed
"...replace that chandelier in the kitchen..." 
tanstaafl.
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