1965 Dodge Dart Charger

I'd say that black piece is like the other sound insulation material you've found elsewhere in the car. Of necessity, it had to be thin, so applying that tar-like coating to it, would help with noise transmission through the unibody. Didn't you find something similar at a building material store?

As for the mat, I'm guessing that's the date of manufacture (8 22) with 1 being the shift and 1648BX7 being the part number. Not sure what the small "H" would represent.