axy

How so?

Isekai = “another world”

It literally just means a protagonist is transported to, reincarnated in, or trapped in a parallel universe. They end up living in a different world than the one they were born in.... That’s it. The method doesn’t matter. You are getting hung up on reincarnation rather than Isekai.

Since it's about the animes let's solely look at the animes.

Remember, overlord doesn't have a reincarnation either. He literally got stuck in that world after the servers would shut down but something different occured.

This is where sword art online has an even more clear Isekai than overlord. First season, death in the game is death in reality. He lives his life there, in that world, one chance. In overlord there's been many times in the anime where he keeps repeating the same question to himself. If he dies, will he truly die? Even in the Alicization arc it's an even more clear Isekai. His entire consciousness, a fluctlight, he was raised anew in that world. It's literally him being born according to his memories in that world. Forgetting he was Kirito from the real world.

I can't defend DanMachi

The "Is it wrong to pick up girls in a dungeon." That's just the thematic similarities. Like calling solo leveling an Isekai. It's not a bad anime, but if they wanted another Isekai on the list I'd say Log Horizon is a pretty fun watch. Overlord + reincarnated as a slime = Log Horizon to me. There's stuck in a game, figuring out the world mechanics, but also politics and empire building.

And yet, my number one Isekai is always No Game, No Life. The most classic non-reincarnation Isekai.

So... While The Water Magician is also a good one... Solo Leveling made me buy the omnibus as soon as it was out to read the whole story. No other anime has ever made me read their novel, manwha, manga, web toon or anything. So, in my personal opinion it still takes the win for me.

I've been watching anime quite a while now and I have some favorites but even those didn't bring me to the point of wanting to go read the material.