Welcome to the forum. Your toilet does not have an overflow (other than onto the floor
). Once the black tank gets full, the toilet will not empty when the pedal is pushed.
I have a very similar SLIDE-EZ valve on my '67 Airstream, and it does not have the fitting pictured in the top, left-hand corner of your picture. The only thing I can think of is that, since your valve is mounted horizontally, the mystery port is a vent for moisture that gets trapped between the plastic & stainless parts of the valve. My valve is mounted vertically and serves to drain the black tank.
Hopefully others will chime in.