Wow. Never seen anything quite like that before.
As far as the action, it looks like it may have began life as a single-shot shotgun, which brings up the first question: is the inside of the barrel smooth, or does it have rifling (spiral grooves cut into the metal)?
Second question: is the reddish ring on the muzzle soft, like leather padding; semi-soft, like rubber; or very hard, like rigid plastic? Or something else? Did you call it a compensator for a reason, or is that just what you thought it looked like?
If it DID start out life as a shotgun, or was made by a shotgun manufacturer, then there may be identification markings on the underside of the barrel. To see the area where these markings might be, you'd have to remove the barrel, which would probably require removal of the wooden fore-end, probably held on by a screw or some sort of spring-latch. Once the wood is removed, open the action carefully, supporting the barrel with one hand, as without the wood to hold it in position, it may be lifted (or fall right off) the action's hinge pin. Roll the barrel over and check for markings or symbols on the bottom, or on the part of the receiver/action that was previously covered by the barrel.
I've never seen a muzzle device like that one, but I am intrigued by its purpose. It is angled, and looks to be padded, which might suggest the device (and therefore the gun's muzzle) was supposed to be placed against something that might be damaged if the padding were absent. Or perhaps it the padding was supposed to "grip" a surface; to prevent the muzzle from slipping-off an object which might be moving, or slick. Based on this, it might be a nail-firing gun, or perhaps a gun used for slaughtering large animals, or perhaps a gun designed to throw objects (using a blank cartridge for power/thrust). All this is guessing, of course, but I am interested in hearing more about the device.
I should also mention, if it originally was constructed as a rifle or shotgun, and was shortened after leaving the factory, in the USA (not sure where you are -- you don't have to say) it may be considered an unregistered SBS or SBR (short-barreled shotgun or short-barreled rifle), or AOW (any other weapon). It may be legal if it is old enough to be considered an antique, or was previously registered by another owner, but in the meantime, I wouldn't go around showing it to strangers (in person, like a gun shop) and asking them what they think it is. The front end definitely looks modified to me, but the rear grip looks very well done (not a normal "garage/basement chop job"), so it may have been manufactured originally in this configuration. Hard to tell just by looking at photos.
"Placement is power" -- seen in an article by Stephen A. Camp
(RIP, Mr. Camp; you will be remembered, and missed)