I've three M11s in the house, two with the "game etching" receiver. The 12ga (serial # 729xxx) says "The Sportsman" on the bolt, not on the receiver. The 16ga (serial # 1,538,xxx) has the same etching, same stock checkering, but says Model 11 on the bolt, in the same location that the 12ga says The Sportsman. Neither says Model 11 on the actual action, just "Remington", the patent #s, and the serial number. The old 12ga (serial # 276xxx) says Model 11 on the receiver (in the location the other two say "Remington") and the barrel, with the Remington trademark on the receiver tang.
I know this doesn't necessarily answer your query, but I've always associated the receiver etchings with the Sportsman version. I would assume that if it has the etching, but lacks the actual distinction on the bolt, it was probably done as a cost saving measure by Remington. Short of a query to Remington themselves, we may not know the true answer.....
Kaiser Norton