Just to clarify-- It won't recognize TB3 or USB-C as a port for video *when connected to another computer via its TB3 or USB-C port* because the computer isn't sending a video signal to that port.
Even if the cable or port you're using is capable of sending a display signal, like displayport, that isn't going to be interpreted as video on the other end of that cable, because your computer is not a display or a capture device.
If, theoretically speaking, you had a video capture device, like a capture card or a camera that connected via USB-C or thunderbolt, that had a video class driver for it that MacOS recognized, presumably that would be seen as a video source. But you can't just connect two computers this way and get a video signal-- the other end of the cable has to be sending a video signal, and generally that either means the other end of the cable is a capture device or a camera.