This topic may be old but here is my take.
Many people were saying that LoS should not be a CV title since it doesn't resemble any CV element except for the fact that the MC is a Belmont. That's not true. Yes, many elements are new on the series, but it still feels like a CV game to me. Here's why:
The Stage System
Older Castlevania (Classicvanias) are played with simplicity. Just whoop some baddies, reach the finish line and beat the boss. This game have the same formula. Beat the stage to proceed to the next one.
Stage checkpoint
Another element from Classicvanias. You restart from the last checkpoint if you ever fail the level by either getting fall from a pit (in this case you only take damage) or simply get beat up by baddies.
Subweapons
This element never left any CV title and LoS is not an exception. You get to use things like dagger and holy water. Maybe some hack n slash games have this feature but I think it's still different. Look at DMC. He use guns as subweapons and we never see this thing on a CV game as a subweapon.
Platforming
Who said LoS was just a pure hack n slash game without any substance? You need to jump to some platforms to reach certain areas. This were not much on a factor on the previous CV games but you will see Gabriel swinging with his chain just like Simon on CV4.
Backtracking
A feature started in Simon's Quest. Unlike CV2 or any Metroidvanias, you don't return in some level because you can't reach some areas of it but rather you have to master it to obtain some power-ups. Like Rondo, you will find some areas for an alternate route. In LoS case, this means new moves for Gabe.
The Gothic Horror theme
You will see enemies like werewolf, vampires, demons and stuff. That's what Castlevania is about. Unless you prefer the anime themed one (Legends, RoB, DoS and PoR). This is a standard element for a CV game.
Generally I doubt you'd get much disagreement on the idea that some CV games in the past have had some of the individual bullet points, but where you'd get disagreement is on whether some of them are necessary or relevant to something feeling like CV. People's complaints are generally outside those items, with the exception of the gothic horror issue, where some dispute whether the designs are close enough to past CVs.
The fact that some of the earliest classicvanias had no backtracking points it out as unnecessary.
The fact that Metroidvanias can feel like CV games without really possessing a stage system, a checkpoint system, or subweapons (some didn't have subweapons, some did) is sort of a testament to the fact that those aren't really necessary either.
That leaves platforming and gothic horror. This means four of those things LoS borrowed that you listed are not really necessary for something to feel like CV.
It also isn't that the stuff you listed doesn't exist, but the reasons why it doesn't "feel right" to people tend to be in the details and the execution, like divorcing a lot of the platforming segments from the combat (a smart move for not making them frustrating in 3D, but a bad move for trying to mimic the feel of a 2D platformer), making a lot of the platforming wall-scaling (which adds believability but takes away from it feeling like the type of platforming of 2D games which doesn't usually mesh with realistic environment design), using a combat system that doesn't even try be like 2D combat, and introducing new elements that some feel are "foreign" to past CV canon--like Pan, "the old gods," etc.
It's not disputed that LoS has stages or platforming or that it borrows elements from past CVs, but rather people's grievances are rather different. Some don't like that the gameplay doesn't feel like the older 2D games (and how can it? It's 3D combat and 3D platforming, which are going to be different from 2D combat and 2D platforming, almost no matter how you do it, and sometimes radically different depending on how you do it.) Some don't like that the world and monster design feels more traditional fantasy-esque than typically was the case. Some don't like that the music was changed to a more "movie-like" orchestral tone. Some don't like the fact that Dracula is in his nascent form rather than his complete form (which couldn't really be helped given the overall storyline placement of the game). Some don't like a combination of all of those or other things yet unmentioned.
Characters
There are some returning characters from previous games like Conell and Camilla.
Those aren't really returning characters (in an alternate timeline, no characters can really be returning ones), just reused names for totally different characters. Brauner (which you didn't mention) and Cornell especially. They almost couldn't be more dissimilar from the characters they're referencing--they probably would've been better off with different names. Camilla, however, might be close enough that it isn't a problem with her having that name--at least I haven't seen any complaints about it like I have with Cornell and Brauner. This seems to be a barrier to you understanding the perspective of the "doesn't feel like CV" camp--noting the surface layer but not noting the differences in the details.
Being able to play a Belmont with a whip is CV-isque enough for me.
I assume you mean as far as characters rather than overall, to which I'd say not even that is required--there are plenty of CVs now where you don't play as a Belmont. Giving a character the name Belmont and making a whip his main weapon is an easy and concrete measure. In contrast, making one game feel like another with required dimensional (3D vs 2D) and representational differences (high-poly models vs sprites), that enters the realm of the intangible. That's hard.