What are you basing this definition on? A rudimentary google search for a definition gives more than one answer and yet none of them have "always online" as a requirement for something to be live-service.
Hitman 3 for example is an example of a singleplayer live-service game, Paradox games like Stellaris are basically that as well, and Minecraft and NMS are often used as examples too. Nobody claimed that a game needs to be online to be updated, that's ridiculous, so not sure who was that clarification meant for.