Unfortunately, there is not currently a way to download an individual's video snippet. There are a variety of free screen capture programs available online that you may be able to use to capture the video. Depending on the program, you may not be able to capture the sound as well.
WARNING: Use caution when downloading freeware from the internet, as it may carry viruses or malware that could infect your computer. Ensure that your virus protection is up to date, and scan files before opening them.