The LeMat fires from the top chamber (or from the central shotgun chamber around which the revolver rotates). The Rhino from Chiappa Firearms is another revolver that fires from the lower chamber, though of course it is just as modern.
Interestingly, Ed Harris' character in the recent Westworld reboot on HBO uses a LeMat replica modded to take brass cartridges. It is as devastating as you would expect a cinematic revolver/shotgun to be.
I think that the Mateba is a real firearm that was then used in GitS, not one that was invented in GitS and then made into real steel. I could be wrong. However, Masamune Shirow is really, really into guns.