The ones in my 1965 looked similar, but clearer and no center logo. I took them out because they gave a strange plastic smell. Strange that they would still be out-gassing after almost 50 years, and no longer that new car smell.
Here's the close up. I also found the build sheet for the parts car. That big bright circle is a cd i just bought that has all the 1968 Chrysler dealer part numbers. Cool.
My experience tells me that these are aftermarket. I cannot ever remember a Imperial bird on any year of Imperial floormat. The New Yorkers of the 70's and 80's had no model designation on them that I can remember. There is nothing wrong with aftermarket ones, condition (front and back) will determine value.
This center emblem design simply looks to amateurishly executed to be a factory approved accessory IMHO, but I'd still use it as a period correct item if it fits the interior color.
Maybe these eagle mats were used in FBI cars.