A voice actor cannot record an audiobook version of a book without the owner permission. A baseball player can sell a recording of a game of baseball (for the sake of argument, since baseball isn't copyrighted)

A streamer playing a game is much more like a sports professional than an audiobook narrator. For most popular streaming games like LoL, Rocket League, Fortnite, Counter Strike or Hearthstone the game itself is mostly a set of rules and an arena.