Basically, NO! . . . unless many things were changed.
Usually there is only one person in the whole world who travels around
Maybe the player almost never runs into any such person, but one of the more interesting features of Nethack and others is that you can encounter the bodies and/or ghosts of your (or on a shared computer, others') previous characters. Also, although you didn't list it specifically, in Dwarf Fortress you can (with difficulty) retire and then rejoin your characters to form a group of adventurers. Also the background text. character class descriptions, hall of fame, and the shopkeepers etc all acknowledge the existence of adventurers as a class, even if during gameplay, there are pretty much not multiple adventurers running around at the same time, and certainly not wiping out the dungeon ahead of you.
That being said, some aspects of this I feel are reasonable, and others not. Certainly adventurers may be rare... they probably would be. And, given what happens to the world when an adventurer goes out and doesn't get killed right away, there HAS to be only a very rare number of such adventurers, or the world would have been purged of monsters long ago.
Which leads to one of the most implausible things to me, which is simply Dungeons & Dragons-style hierarchical character improvement power levels. The conceit started with that game and copied by huge numbers of games, is that trained human warriors start out slightly better than minor opponents, but hopeless against medium monsters, and that by killing a dozen or a few dozen monsters (and healing amazingly quickly between each battle) they can become ever more powerful on a very steep power curve until eventually a hero is about as powerful as Superman, but the world is full of still more super-monsters, etc etc. Which is basically ridiculously implausible and unsustainable, at least in the way it is typically implemented in such games. However, if those mechanics (which involve killing hundreds of foes and somehow gaining a superhuman ability to sustain injury) were replaced by something involving skill and intelligence (where characters learn how to survive by being smart and avoiding combat and injury almost always), there might be some hope for an actual world with highly-experienced adventurers not requiring superhuman powers nor annihilation of hundreds or thousands of victims per hero.
These monsters may drop items that sometimes do not make sense in the
context, either due to the items size or the monsters typical eating
habits. An example would be a bat dropping an Iron Sword or a Wizard
dropping a suit of Iron Armor.
This is a good point but is less sloppily done in Roguelikes than it is in their action derivatives such as Diablo, Dungeon Siege, Torchlight et cetera, in which animals drop human equipment. I think the best explanation here is that usually this should not be taken to mean that the handless unclothed monster actually had a suit of armor or whatever, but that such loot were nearby to where they were encountered, and is only findable after the monster is slain... possibly again items lost by victims of the monster. However I feel this is a concession to sloppy game implementation. Often in Roguelikes the loot is just lying on the floor near a monster, which makes more sense.
As for world plausibility, it would be realistic if the treasure found were all remains discarded and scattered from previous adventurers or original inhabitants of magical strongholds... but the way these and other games tend to have so much treasure lying randomly everywhere... no, that seems almost impossible unless a dragon hoard, battlefield aftermath AND a wizard's guild storehouse were distributed by a few years' scattering by the Bat monster from Atari 2600 Adventure. The weapons and tools are far more plausible than consumable magic items such as potions and scrolls. To see what would be plausible, play through a dungeon and then wander back the way you came, looking at what you left behind. Of course, there would also be more stuff left behind if the game didn't allow the player to carry an implausible amount of junk with them.
All the other characters in this world just stay in the relative
safety of their town or towns.
That sounds extremely plausible to me, and is what most people do on earth all the time, and especially is what most people did during the corresponding time period.
Somehow they are able to survive in an
economy based entirely on the loots of the lone adventurer.
It never occurred to me that the adventurer was keeping the village alive with his loot - in which game did you see this? It seems clear to me that the villagers in these games get their requirements from non-adventuring activities, and that economy in the modern sense has very little to do with it, let alone the adventurer.
The adventurer in a Roguelike can usually join them by leaving the dungeon or adventure area, at which point they generally get a hall of fame entry saying they retired or whatever instead of that they died.
i.e. In our plausible Roguelike world, they would farm and hunt and fish and craft in safe places that might or might not be shown in the game (which tends to omit or downplay safe places to focus on the adventure).
There is an infinite amount of loot in the world. Typically the deeper
you go underground, the more likely the magically enhanced loot will
be dropped by the monsters. Those monsters also get tougher and more
fantastical the deeper underground you go.
I was about to say that it wasn't really infinite, but then I considered that not only do some Roguelikes have some regenerating Infinite Dungeons (e.g. some places in ADOM) but practically all such games do have randomly generated monsters that appear as the hero wanders around, and they do generally have a chance to drop more loot.
I would say that the thing that is most implausible about that infinite regeneration, is the rate at which it occurs, as well as the general absence of any findable path by which the newcomers could appear. The most plausible way I can think to explain that is they must be entering from passages the player has no access to, or they are being teleported in by dark magic.
It might be seen to make some sense that the more powerful monsters would be lower down and have more valuable loot, especially if it were provided by previous dead adventurers, the better ones making it further down before dying and leaving their gear. However that doesn't help explain why newly-arrived monsters, particularly ones with no way to carry anythings themselves, result in usable equipment such as a suit of armor or magic book when slain.
What WOULD make more sense, sort of, would be:
1) If the better equipment was actually appropriate to and being used by the better monsters. The Death Knight probably does have some interesting weapons and armor, some of which might still be usable after beating him.
2) The reason for this dungeon existing and having monsters might be some wizardly alliance or demon sect or something that intentionally populates and equips the dungeon, putting more common beasts up top to stop intrusion without raising too much attention, while the lower levels are filled with more serious creatures with supplies that they are supposed to use on intruders. However these should be more organized than the random distribution in most Roguelikes, and they should tend to mainly be using that equipment against the intruders, rather than leaving it unused for the intruders to prosper with.
Is there any plausible explanation, whether fantastical or scientific,
that could describe how a Roguelike RPG world could exist?
Again, I think the only real way to explain the type of world, would be to change the mechanics as presented in the games. The time scales are all wrong, as are the power scales, the carrying capacity of players, the usual layout and monster/loot distribution, and so on. I think though that you could correct many of those things and still have a world that is fairly similar to many aspects, but be much more self-consistent, sustainable and even almost plausible.
I think one really needs to fix the holes in cause and effect before one could get anywhere. Why are there underground complexes? Some make some sense - there are mines and temples or even underground cities created by magic. That's no so bad. But what's living in there, why, what are they doing, how do they interact with each other, and the villagers survival makes sense - what are a random mix of monsters doing that has them manage to co-exist underground and have enough food and water and air and shelter? There can be good answers to those things, as seen in more thoughtful/realism-oriented RPG published adventures (generally NOT D&D, but some are better than others even there).