Could you explain how one would go about determining what you explained here? Is the "KLE..." part of the shortened URL just compressed somehow and you can decompress it? I guess I always assumed the browser just requested the shortened url and the black-box google server opaquely serves up the destination page, allowing it to do whatever with the (I assumed, incorrectly it would seem) unique string in the URL. Unique to the user sharing and video being shared, I mean.
The KLE portion you're referring to is the video ID. It's how the video is uniquely identified. It's not compressed or storing any tracking information about anyone when it's shared. You can see that in both URLs it's the exact same value.