Part of the reason for the confusion is that this is a retcon of sorts. ECS was first described (with a different name) in a postmortem of Dungeon Siege, but as far as I'm aware, the modern usage of "system" was coined by Adam Martin during the development of Operation Flashpoint: Dragon Rising.

There are good technical arguments for making systems into first-class values, of course, but this interpretation will always be in competition with the older one.

Interesting. The reason I find it worth pointing out is that the "entity" and "component" parts are not really that interesting by themselves. You could have an object-oriented "entity-component" system where components encapsulate game logic, for instance. It's the separation of game logic into the separate "systems" that is interesting. That said, the actual implementation of "systems" varies so much that it's not surprising people focus on the "entity" and "component" parts.