The way english speakers use the term ‘isekai’ is different from the way japanese speakers use it, & japanese speakers actually categorize things a little bit differently. Most of what we call ‘isekai’ would be referred to in japan as ‘narou-kei’, because most of it comes from light novels that were originally published on a site called “let’s write a novel”. These light novels were generally written around the same time as the Sword Art Online books, and were officially published in the wake of SAO’s success — in other words, they come from an insular community & were selected for promotion based on their similarity to another work. Actually, a lot of narou-kei are basically Dragon Quest fanfiction with the serial numbers filed off, & some folks (including youtuber Pause & Select) suggest that narou-kei authors are disproportionately folks who would rather be writing an indie RPG but don’t feel like they have the time. Both english speakers and japanese speakers seemed to start using ‘isekai’ as a genre name around the time that SAO spawned imitators, but in japan it’s much more of a description, because its meaning is immediately understandable. Japanese audiences would distinguish between narou-kei and isekai, even though they very often overlap, & so they don’t have trouble with cases that are one but not the other (such as Danmachi, which is very clearly narou-kei, or Escaflowne, which is very clearly not narou-kei).

The english language actually has its own word for this type of story: the ‘visitation narrative’. It’s been around for a while (like, since the fifteenth century at least), but was mostly limited to utopian novels until it had a resurgence in the science fiction and fantasy pulps of the 20s and 30s, & both Edgar Rice Burroughs and H. P. Lovecraft wrote extensively in this genre (in the former case, with the John Carter series, and in the latter, with the character of Raymond Carter in the dreamlands stories). From there it influenced D&D, and it looks like the influence of D&D on computer RPGs is the means by which it made its way into the narou-kei community.

What characterizes narou-kei? A world that has a generic western-fantasy feel, usually specifically with Dragon Quest elements; game-like (and especially RPG-like) rules and mechanics; an overpowered protagonist with a harem. Almost all narou-kei stories have these elements, while other isekai stories (even with a western fantasy setting, like Escaflowne) don’t. Narou-kei is intended to feel like an imaginative retelling of a play-through of a JRPG, and this means the idea of a visitation narrative is fairly natural & blends well with being overpowered or a ‘chosen one’: the protagonist is identified with the player character, which is to say, with the author himself (who is describing an imaginary ideal playthrough of a game that doesn’t exist). This means narou-kei is actually well within a certain tradition in anime & light novels — the long string of books later made into anime that are transcripts of the author’s D&D campaigns.