Fullstory playback should capture user interactions with videos that are a part of your site, with a few exceptions. Fullstory does not capture the video itself.
If you have an embedded video hosted by YouTube, Wistia, or similar services you may notice that user interaction is not captured and seen at time of playback. This is due to the content being housed in a cross-domain iframe. If you don't have control over the iframe contents in order to insert the Fullstory script, you won't be able to watch user interactions with the video during your playback. Read more on capturing iframes here.
Fullstory offers minimal support for the <video> tag. Meaning, Fullstory will capture that the <video> tag was added to the Document Object Model (DOM), but it doesn't offer additional functionality such as sync playback with the timeline, etc. If the video has the autoplay attribute, the video may appear to play during session playback.
Will Fullstory capture the sound within <video> tags?
If your site contains <video> elements, and any of these contain audio, then this would likely also be heard in Fullstory as we are capturing the entirety of the elements on your site (unless they are blocked from capture via privacy rules).
If you wish to exclude such video elements entirely from capture, you can add .fs-excludedirectly to the <video> elements in your code to stop these from capturing in Fullstory moving forward. Or your Admins can add an in-app privacy rule for video to achieve the same (block capture of video elements).
On the other hand, if you do still wish to see these videos in Fullstory playback, but would rather just not here the sound - it is usually possible to mute your Fullstory tab/window directly in your browser.