What I contend is that "when you lose you start over" is the ONLY defining characteristic of what people lately call a "roguelike". And it's not even applied consistently!

The term is self-descriptive. It means "a game like Rogue".

Lately, the term has been latched on to by people who don't know what it means. They latched on to it probably because they thought it sounded cool, or saw a game on Steam with the "roguelike" tag that was fun. Let's examine just how many genres the term encompasses:

Isle of Arrows (https://store.steampowered.com/app/1946970/Isle_of_Arrows/) is a tower defense game. It's tagged as a roguelike.

PlateUp! (https://store.steampowered.com/app/1599600/PlateUp/) is a game about managing a restaurant. It's tagged as a roguelike.

Nimbatus (https://store.steampowered.com/app/383840/Nimbatus__The_Spac...) is a game about building space drones. You can compete against other players or play in sandbox mode. It, SOMEHOW, is tagged as a roguelike.

Brotato (https://store.steampowered.com/app/1942280/Brotato/) is an arena bullet-hell game where the only randomness is what items and upgrades you're offered. It is tagged as a roguelike.

Vampire Survivors (https://store.steampowered.com/app/1794680/Vampire_Survivors...) is another arena bullet-hell game and there is almost no impactful randomness. You have a very high degree of control over what your build looks like. It's tagged as a roguelike.

Slay the Spire (https://store.steampowered.com/app/646570/Slay_the_Spire/) is a deckbuilding game. It's tagged as a roguelike.

Dome Keeper (https://store.steampowered.com/app/1637320/Dome_Keeper/) is a base building game. It's tagged as a roguelike.

The Van Game (https://store.steampowered.com/app/2081860/The_Van_Game/) is a game about traveling to national parks. It's self-described as being inspired by the Oregon Trail. Was the Oregon Trail a roguelike? The Van Game is sure tagged as one.

Another Farm Roguelike (https://store.steampowered.com/app/2116850/Another_Farm_Rogu...) is a farming sim. It even has "roguelike" in the name.

Risk of Rain 2 (https://store.steampowered.com/app/632360/Risk_of_Rain_2/) is a third person shooter without procedural generation. The randomness is in the equipment you find. It is tagged as an action roguelike.

Darkest Dungeon (https://store.steampowered.com/app/262060/Darkest_Dungeon/) is a game with a long progression arc. There is randomness but no main character. In fact, your characters can die and you don't game over. Your entire PARTY can die and THAT isn't game over (https://steamcommunity.com/app/262060/discussions/0/61282346...). It, too, is tagged as a roguelike.

Caves of Qud (https://store.steampowered.com/app/333640/Caves_of_Qud/) is a roguelike. Like, an actual one. It's tagged as roguelike AND it's also tagged as "traditional roguelike". Which is yet another indicator that the term simply doesn't mean anything of significance anymore.

Why does nobody describe action RPGs played in hardcore mode (e.g. Diablo and Path of Exile) as roguelikes? They fit both of your criteria.

How come roguelike is not associated with games like Fortnite or PUBG? Again, both games provide a good deal of randomness and character building.

We have games from nearly a dozen genres that are described as being "like Rogue". Some games have a lot of randomness, some don't. Some games described as roguelike _don't even feature permadeath_. And some very popular games with impactful randomness and character building ARE NOT described as roguelikes.

The term means literally nothing.