That's a paper-weight glass not a furniture coaster.
As to fantasy vs real take a close look at the image with a magnifier, if you see dots it's a printer created image and thus definitely fake. Originals would have been lithograph. It could also have been made by taking an old ad of original origin and placing it under the glass. Remove the felt and check the paper, most were 110# or heavier cardstock to handle the litho print. And it should be a perfect diecut circle, no rough trim edges like from scissors.
Paperweights like ink blotters were a common item you'd find in an office in the bygone days so real ones do exist out there.
There are no little dot's, appears to be a lithograph also it's impossible to show in photos but if you look through the base of the glass you can see that's it's heavy cardboard/cardstock, definitely not a thin magazine clipping or something like that. I don't want to try and remove felt because it has never been tampered with, if I try and "peel" it back it will tear.
