I recently played a pretty decent game that was a card game in its essence. They called that one a roguelite due to essentially its bones files. But it’s a card game, not really an RPG even. Rogue is a very specific style of RPG. So what’s the definition of roguelike and roguelite?
It's both an incorrect term (because, as you mentioned, the overlap with rogue is limited) and absolutely the correct term (because people generally understand what it means, even if they've never heard of rogue).
I think it's important to remember that language evolves, it's more important to be understood than to be correct. Shouting into a hurricane isn't going to stop the storm, no matter how right you are.
What other "~lite" or "~like" in the entire language as a similar property of being nothing like the "~" part?
Another common genre is Souls-like, stemming from the mechanics of Dark Souls. It's a term for a game that has bonfire like mechanics, high difficulty, punishments on death, etc. There are many games that are souls likes that share none of the visual themes or moment to moment combat mechanics of Dark Souls.
And as several other people have commented, the games are similar to rogue, just at a higher level of abstraction than you are looking at them.
* Permadeath / "ironman mode", generally enforced by the game
* Procedural generation of game levels/encounters
* "Progression" elements, where the encounters get more difficult but the player is gaining resources to allow them to overcome those challenges (as opposed to simply gaining mechanical skill at the game)
These three elements combine to make a game where you lose early and often, but starting over gives you the opportunity to experience the game differently, due to the procedural nature as well as because you have the opportunity to invest your resources differently, hopefully making better decisions.
I don't think they need to be strictly RPGs, but the progression elements are key. Those elements are present in FTL, for example, if you consider that the ship itself is the main character.
For example, Rogue Legacy is almost entirely focused on metagame progression between runs, whereas your character barely develops at all mid-run. Classic rogue-lite.
I personally don't think the distinction matters that much, except to pedants and purists.
[0]http://www.roguebasin.com/index.php?title=Berlin_Interpretat...
Just like there are people who care about the definition of 'roguelike', there are people who care about the definition of 'rpg'.
Whether the genre is RPG, action or economical simulation doesn't matter nowadays. The only relevance is whether there is a complex gameworld, to tell apart from the simple randomized game-boards which solitair or bejewled offer.