Why? because he isnt a floating legless skeleton with a scythe? what "Death" looks like personified is wholly up to interpretation. not to mention we never see his actual face due to the devil mask. all the other necromancers totally look like the classic CV death though.
now, as to what it has-
A chain whip? yes- Like in many castlevanias. Just not named vampire killer, and given a cross shaped hilt and made retractable.
Daggers and holy water? totally.
Item crush? The dark crystals count as this.
Candles? has them in the castle.
Familiar enemies? Tons.
Familar bosses? sort of, most are complete re-imaginings of the previous character. Evil butcher was originally a stage enemy
Mythos nods up the wazoo? super check. Special mention goes to Rinaldo, and his involvement in making the whip. And the "vampire killer" extension, giving the whip it's trademark name in a way. As well as The castle belonging to the Bernhards and the fact that it is a living entity.
Platforming? yes. much like classicvanias
Familiar areas? mmmm... sort of. Theres a village, a castle, a clockwork tower, and hell. but then theres ruins of an ancient civilization and a forest, which is kind of new territory. Then theres Crows pass, which is sort of in between. Literally, both ways.
A journey to the castle? AKA the whole game does not take place inside a castle? check. much like a few classicvanias.
The Belmont in question himself? Based on the original "manly" look before they became pretty boys with Richter. He is also based around Simon's outfit from CV2.
But alas, there are no bone pillars. How can it be a castlevania game without bone pillars?
if anything, its the first half of the game until the castle that feels completely foreign.
Also, folks, again, this game was ALWAYS castlevania. It was pitched as such, and developed as such. Konami was just unsure of branding it with the trademark name for a short while and decided to reveal it as simply "Lords of Shadow" so it would be an IP, only later greenlighting the title.
Right from the Cox himself.