clarry: rjbuffchix and clarry, the two who were having this discussion.
teceem: rjbuffchix seems to be an individual that doesn't want to be joined at your hip. But I'll let him confirm that.
Confirmed :)
I do (like to think I) get clarry's point.
The reality is that there are games which say "LAN" that doesn't mean what I would take LAN to mean. There are also games which say "multiplayer" that may actually include what I would want, though in my experience this is usually obfuscated or not advertised at all. And, as discussed in this topic, there are even games which say "DRM-free" that doesn't mean what I (or, in my reading, FCKDRM.com too) would take "DRM-free" to mean.
Seems best to me to work with the common connotations of words, with the acknowledgement that precise language is important due to companies misconstruing the terms (sometimes this even seems purposeful imo). With that in mind, "offline multiplayer" is the best "catchphrase" I can think of that encompasses what I am looking for developers to include in games. "Offline multiplayer modes, in addition to online" is more a mouthful but also works to some degree.