Access to an online server is clearly a service, hence the word "server"
replyThe discussion is not just about online multiplayer games though, it’s about games in general. There is no good reason why buying a singleplayer offline game need be a “service”.
replyThere IS a reason they don't make it possible to download the game copies directly, which is it becomes trivially easy to perfectly replicate and distribute new copies online, which is not true of any physical good.
replyPeople who aren't overly-online forum denizens only care about this issue insofar as it affects them, and the only way it affects people in the real world is when they lose access to online games when the server shuts down. Offline games don't get access revoked in practice.