The Cybershot's design makes it impossible to use as a webcam when connecting the camera by USB cord to a computer. Recording video while the camera is connected to computers via USB is not supported.
Cybershot and USB Connection to a Computer
Connecting the Cybershot via USB cable to the computer and powering on the camera automatically causes the camera's memory stick to appear on the computer as an external hard drive. The lens of the camera remains closed, making it impossible to record video while the camera is connected via USB.
Webcam Software and the Cybershot
USB webcams are recognised as video hardware by the computer and by video-streaming software as a valid source of live video. Video-streaming software can't recognise a Cybershot because the computer sees it as a data-storage device and not as a video-capture device.
Alternatives to USB
Some Cybershots have video out jacks; coupling it with the computer's analogue video input jack allows it to be used as a webcam. This method is completely different from using the camera as a USB webcam device.