The problem I see with this definition is that we have things called RAG agents which don't technically act in any environment except for provide information.
Is that not a summary and translation agent? For some reason only the user knows, they do not want to or cannot read the entire RAG source, so they use their summary and translation agent to give them summaries and to translate the technical jargon they do not understand. That Agent becomes a teacher of the RAG source. I see no problem with the Agent definition when given this perspective.
Is that a problem with the definition of agents, or a problem with sticking the word "agent" on something that doesn't meet the definition of an agent?