If I play Destiny 2 on my twitch stream, at the end of my stream, my audience has watched a video. Someone recording my stream has a copy of a video that I have produced. Bungie’s copyright is for a game, not a video. My audience does not have a game. My audience cannot play their “copy” of Destiny 2, because what they have is not a copy of what Bungie holds the copyright to.
I hold the copyright to my performance, not Bungie. The movement of my character and the sound of my voice are under my control, not Bungie’s.
You are correct about a public performance of a song or video, but not a playthrough of a game.