Rogowski coil output resistance series or parallel
The 50&Omega; resistance you measured IS the series resistance (source resistance) of the coil. Why would you think otherwise?

It is there to provide a good match to the cable, eliminating potential reflections that would confuse high-speed measurements.

You use the 50&Omega; termination on the scope for the same reason.

This combination of source impedance and load impedance creates a voltage divider that always results in a 50% reduction in voltage when compared to the open-circuit voltage. Sometimes test equipment takes this into account when displaying the data; sometimes it doesn't.