I stream gameplay to YouTube and sometimes moments happen during gameplay that I feel would make a good GIF. I don't want to download the entire video just to make a 15 sec GIF. What do you think would be the best way to isolate a short clip from a long stream video?
YouTube has/had an experimental feature which allows the creation of GIFs via the share button, but it's currently only enabled on select channels (example: vsauce3) and only in the old design.
Other than that, if you want to produce highlight clips, you can import your stream into the YouTube editor which allows you to create a new video (a gif with sound!), or you can use third party services like GIFs.com or imgur.com.
The YouTube Live team is also looking to create better tools for streamers to enable things like that, so it may be that in the near-medium future there is going to be a better solution.