That cable was used for a few years circa 1959-1962. If it is original to the premises in question and is properly grounded where that circuit receives it's supply, install the receptacle with grounding prong. The 16 gauge ground is electrically adequate for the purpose on properly protected circuits. The reason for the later upsizing of the equipment grounding conductor is that the 16 gauge was too fragile for the typical handling involved and was sometimes broken during installation of the devices.
It is surprising that a 2-prong receptacle was used with that cable .
Handle it carefully

"It is surprising that a 2-prong receptacle was used with that cable "

In the 1959-built house that I grew up in had grounded wire to convenience outlet junction boxes. There were, however, no grounded convenience outlets installed, anywhere. We installed them some time after that as needed. Later in life, it was quite a surprise (shock) to me when I discovered that most of the two-prong outlets that I was later exposed to did not have ground wires available in the box ":-0 I was quite traumatized by the experience.

The 240V dryer outlet did include a ground conductor. The metallic ceiling boxes in the basement had the ground wires terminated by winding it neatly around the clamp screws or clamps somehow. (I don't remember all that detail.) I don't know about the 240V range outlet or the ceiling boxes in the finished part of the house.

These transition times can be most interesting. Perhaps the wires and boxes were required to be grounded, but the electrical supply house did not have any :o plugs that day so they used :