DoomRL uses copyright protected sounds and trademark protected logos and names. The ascii art in descriptions probably counts as derivative works too. If ID wished they could enforce their rights and send Kornel a cease & desist. They could try suing for damages but I doubt a judge would find that any losses were incurred by the violations.
There is a thing within copyright law called
fair use, however, and while DoomRL wouldn't really fall under any of the reasons for being considered fair usage I would think it also is not an overall offender in terms of the four areas set out in the link above (Purpose and character: neither educational nor profit; nature of the copyrighted work: both games, but very different types of games; amount and substantiality of the portion used in relation to the copyrighted work: sound and music individual copyrights would be violated in full, but that's the full extent of uncontroversial violations (I doubt the images both in descriptions and in-game would be considered infringing, for example); and the effect of the use on the potential market for and/or value of the work (I find the chance that it would be large enough to be seriously infringing highly unlikely).
As for the trademark issue, I found
this and it seems that the big thing for infringing there is not confusing people on who owns the trademark. In the slightly expanded description of what constitutes as a 'nominative use', they mention three things that a person using the trademark in their (writing, but this can be expanded to DoomRL) work has to do to prove they're not breaking the law: 1. The product can't be easily identifiable without the trademark; 2. The user only puts enough of the trademark in the work to identify the product as reasonably necessary; and 3. The user doesn't do anything that would suggest (while using the trademark) endorsement or sponsorship by the trademark owner. #1 is pretty reasonably done IMO, and #3 seems pretty well satisfied (there's no claim made anywhere in the game that id had anything to do with this aside from inspiring it that I've seen). That leaves #2, which toes the line depending on what parts of the game are actually trademarked (if it's just the name that's trademarked, then I would think Kornel's all right; and I think the rest would fall under copyright law, but I can't be sure).
In the end, I've gotta agree with one thing, though (found on the copyright page, which it seems like Kornel's more potentially infringing on anyway): It may be best just to ask id about it and get their blessing (AFAIK, they haven't quite gone down the complete-craphole yet like some [*cough* EA, Sony] companies have, so they should be fine with it).
Wolfenstein 3D doesn't have copyright issues with Doom because it was made by the same people and it predates Doom and it doesn't share any intellectual property anyway -_-
You're right, bad example. Really, I was reaching for an easy illustration, but I could just as easily have said Duke Nukem. As for sharing intellectual property, see above.