I don't have anything to prove that she didn't have -Livesteam on the end of her name or that osu! wasn't in her library. I guess we have to stick to the most likely possible answer which is that I rappled from my creepcopter into her bedroom window and sat in the dark corner of her room for an hour and watched her play osu.
As someone who has serious trust issues, I make it a habit to not lie to people. An example of this would be when I used evidence that somewhat supported you earlier.
You yourself posted an image displaying my previous aliases, one of which contained "LIVESTREAM" and the other "LIVESTREAMING" at the end of my name. I disproved your argument with my side of the story. I'm pretty sure you can't delete things from your alias history, so that helps prove that I have not put "LIVESTREAM" at the end of my name in a while.
Here is a screenshot of what my Steam library has looked like ever since Cybertails gifted me Sword and Sworcery:

I have not added any non-Steam games to my library in a long time, and even if I had, they would have been automatically removed by some sort of glitch that removes any non-steam games a few days after they were added. I cannot provide any solid proof for this, so you'll have to take my word for it.