I feel like Castlevania IV, Dracula X and Adventure have always been Castlevania... Haunted Castle though... well it's good to have confirmation from one of the staff members (forgot to thank you for the info you got from him).
I remember when Lords of Shadow was first teased to the audience, it was NOT advertised as a Castlevania (I have a press kit that has absolutely no mention of Castlevania on it). Later it was announced it would be a Castlevania game, so I thought Konami had changed their mind during development, but in fact it was revealed that it was always meant to be a Castlevania game. Well, that's what a friend of mine said (at the time I still thought it was a non Castlevania game retooled to be one).
It would be amazing if something of the original Haunted Castle remains, like graphics, backgrounds, or even just text information. It's a funny entry in the series, marketed as Castlevania in Japan but as a unique game overseas. It's a great insight into the early years of the series, where marketing and development was super messy and a bit random. I miss those years where Castlevania wasn't such a big deal.