Slash's bullet points do include the game of life, but I don't think there's any reason to argue over that point. The bullet points fail to capture what a roguelike game is on one hand and fail to differentiate roguelike games from other types of games on the other. It has nothing to do with rhetoric.
But sure, let me try to give a definition.
A roguelike game is a computer game that implements roleplaying (in the sense of pencil and paper games like Dungeons and Dragons) game mechanics and content, following the tradition and idioms of early computer games on UNIX and VMS including rogue, moria, hack, and larn.
A "systematic breakdown" is somewhat beside the point, as it would really just be elaboration on the meaning of the words "tradition" and "idiom" as they relate to rogue, moria, hack, and larn.
A couple of things about this definition: First, it can be and often is pretentious to call one's game "roguelike." Roguelike games are not schlock.
Second, a game can be roguelike in large part by virtue of pedigree. For example, if a game is built from code bases that go back to the originals with reasonable continuity in spirit from one iteration to the next, it can be roguelike while differing from the originals in substantial ways. For example, tomenet is obviously a roguelike game, even though it's not "turn based" as understood by r.g.r.d alumni, it's not single player, and its permadeath mechanics are a bit iffy. It's more important to be able to point to how the game fits into previous work in the genre than to tick off a checklist of features.
Arguments about whether a game is roguelike shouldn't be "well, it doesn't have this feature, that feature, and it has this mechanic that's not allowed," as if it's a question of scoring something. The argument against a game should question its connection to existing work, especially the so-called "major roguelikes" (and that doesn't mean spelunky, btw), and what its contribution is (i.e. is there something new here or is it at best an homage?). If it does differ crucially in mechanics, are these differences so radical as to better place the game in another genre or do they address an issue in previous work and suggest a way forward?
You obviously put a lot of weight on the technological origin of Rogue et al. While that's interesting, I don't see how it constitutes the actual gameplay of the genre, much like how modern novels are considered epic literature, even though the earliest epics were part of an oral, rather than a written, tradition. This history of literature's origin is hugely significant, but still, the sorry sods who most assuredly claimed that Gilmgamesh or The Iliad stopped being "real" literature once they were written down, have been forgotten (probably because they refused to have their own arguments put in writing, but that's going off on a tangent here). And there was much rejoicing.
There's an obvious conceit here. Are graphical "roguelikes" (in the sense understood by many here) producing genuine improvement and innovation over more traditional roguelikes? You imply the answer is something like "Oh God, yes!" My answer would be, "Not really." I've played my share of recent games with no terminal interface, etc. I don't see the transition from cavemen sitting around a fire to robed scholars stroking their chins over a pile of scrolls. I see traditional roguelike efforts going on pretty independently of the discussion here and making real strides (see DCSS, Sil) and I see projects with lots of graphics that don't strike me as anything new. It doesn't help that so many of the latter have names like CommercialFranchiseRL.
Anyway, I wouldn't put graphics up there as a matter of definition, but I think a roguelike game needs a reasonable excuse to have them, for example, "some guy from my mailing list put them together and sent me a patch and they seem to work okay and aren't likely to cause trouble down the road, so I put them in as an option." I do think you need a damn good excuse not to have a terminal interface though.
This getting way too long, but two more things about my emphasis on the history and technical origins. These are things that seem to lost to current thinking. First, roguelikes were originally very social games. People played them on multiuser systems at universities, traded war stories, etc. (And war stories, in my opinion, remain one of the best things about the genre.) Then PC users started getting DOS versions via shareware catalogs and some of them seem to have thought that's how it all began. Well, it's not and multiuser systems remain popular and vital. Second, the centralized server-oriented aspect, while just a fact of life back then, represents an untapped opportunity now. There are significant technical advantages to delivering a roguelike game via ssh or telnet, even aside from the multiuser considerations (which are also particularly relevant in the current climate). Telnet is widely available and requires no installation of software. On the other hand, a game that runs primarily on servers can be made of whatever you want -- you want to use an integer programming engine, a numerical linear algebra package, a graph theory package, an image processing library, and ten other things your user is guaranteed not to have installed? You want to use lots of different programming languages, big databases of precomputed whatever? No problem. All your player needs is telnet.