It is appropriate ton separate the acts of
1) Converting an (optical) scene to an electronic signal
2) Recording the signal
IMO, (2) is irrelevant. You totally can have a "video camera" without having any means to record the signal. You still have a video camera, for, for example CCTV for remote viewing. Applications include viewing inside dangerous or inaccessible spaces (pipes or nuclear reactor chambers), and security. I'm sure there are many others. Early TV broadcasts were transmitted live, because there was no means of recording the signal and playing it back later. (Or if there was, it was not practical or economically feasible.)
So I'll agree with Farnsworth or Baird. I don't remember who did it first.