Most likely the video file used in the screensaver is compressed using some video compression technology, for example DivX, and appropriate decompressor (also known as video codec or driver) is not installed on the particular computer. Often you would see an error message saying decompressor not found.
To enable viewing such screensaver you must find out what kind of compression is used in the video file and then download and install the appropriate video codec (decompressor) on the computer having problems with the video screensaver.
Sometimes the problem can be solved simply by opening the file in Windows Media Player which will then automatically download and install the codect. If this does not happen, you can still open the video file in Windows Media Player and on the File menu click Properties to find out what video codec is used.
To find and download the codec you need, please search the web using keywords video codec and the name of the codec you are searching for.