You can only pair one Siri Remote per Apple TV, so if you want to get your multiplayer game on, you'll need to use iOS devices with the Remote app, or buy MFi game controllers.
If you're buying a new Apple TV and want to get into multiplayer gaming, don't spend money on multiple Siri Remotes. You can only pair one (1) Siri Remote with one (1) Apple TV. Instead, you'll need to use your and your family and friends's iOS devices running a (likely updated version of) the Remote app, or better still—made for iOS devices (MFi) game controllers.
Apple does sell the Siri Remote separately, but that's for the same reason Apple has always sold ATV remotes separately: In case you lose or break the one that came in the box.
So, don't be confused and don't be tempted to try it anyway. You can only use one Siri Remote with one Apple TV, and if you want to do multiplayer gaming, you'll need iPhones, iPods touch, or MFi game controllers.