Yeah, I think we're pretty aligned. I just see GaaS as an extension of what people called "MMO-like": the product is meant to be consumed on a daily or regular basis due to ongoing maintenance of a character, world or concept. New content comes out regularly (rather than expansions) that supplements this daily maintenance of the personal character or what the character has influence over. Daily/weekly quests or challenges, time-gated things like Battle Passes, etc.

I agree that the "Service" aspect of this might be where I'm getting hung up, because like, SaaS is about software you don't own, self-host or run yourself. I guess the same thing can be said for all games that are encompassed in a subscription model, because your incentive to keep playing is tied to that subscription. If I paid for a subscription and started a game like Slime Rancher or Subnautica, it kind of *becomes* a GaaS because if I stop paying for the subscription, all that progress and work kind of goes away.

I mostly just am applying what I see with "progress shooters" like Destiny, Warframe, or Battle Royale titles being the prime example of GaaS; repeatable content with progression or maintenance based on external factors (battle passes, prestige stats, loot generation), that keeps going when you're not playing (providing the "rat race" setting to motivate you to keep up).

Subnautica or Slime Rancher essentially "being on pause" when you're not playing only kind of applies when you're not paying for a subscription. They're "still running" as long as your subscription is.