Depends on the camera, if a camera has webcam function built in it's usually nowhere near the quality you would want. For example if your camera outputs hdmi (no copy protection) you can view and record it with pc and possibly use as webcam
with hdmi capture device. Typically gamers use hdmi capture device.
https://www.google.com/search?q=hdmi+capture+card+usb&oq=hdmi+cap Typically you find good reviews on youtube when people review their devices, some people make living only playing games and putting it up on youtube. This also works with composite video, then all you need is a composite capture card, or maybe one of those ati allinwonder display cards.
Most modern cameras should be capable of outputting hdmi.
Also note if they have the video on computer monitor it doesn't mean it's a webcam, they can hook up hdmi lead to a monitor and live view the picture. (I know there are technically retarded people who mix those two things, not saying you are)
You can even live view the hdmi picture from camera AND record at the same time, that could be better than just webcam functionality.
Good quality picture required lot of bandwidth, some cameras have something like this built in, but don't expect anywhere near the same picture quality what you get with when normally using the camera.