I disagree that "hören" can mean "hear" and "listen." I think German does make the distinction that LB_StorM draws attention to in English. I think that this sentence would definitely imply that he is deaf, or at least that the sound waves are not reaching him, for whatever reason. If you wanted to say "He does not listen", "Er hört nicht" would sound incomplete to a native speaker. "Er hört nicht zu" would make it clear that he is acoustically hearing but not listening (in the sense of obeying). You could also use the preposition "auf" if there is something specific he is not listening to: "Er hört nicht auf mich" -- "He doesn't listen to me."
"Er hört nicht" means "He doesn't listen" in the sense of "He doesn't obey".