Well, it's fairly simple yet utterly stupid of YouTube not give the option where it should be.
The option is actually in the Dashboard and not present in the video manager where it should(also) be.
Now in order to change the game name in your stream head to YouTube Dashboard by clicking other features > More.
Or you can also click this link. https://www.youtube.com/dashboard?ar=1&o=U
Now click on LIVE STREAMING in the left menu and you should be able to edit the game you're streaming.