Dracula mentions Lisa in SoTN. He even asks Alucard upon his defeat what her last words were, validating Alucard's presence at her burning.
Also, again, even if Dracula has vampiric traits by Sorcery and alchemy, he is STILL a vampire. He is an immortal who drinks blood, can turn others into vampires, burns in sunlight, (according to some of the games and popular culture, although it contradicts Bram Stoker) Is weak to holy weapons and items, etc etc. He has all the traits of the Vampire. Even though he was not sired and brought about his transformation through alchemical means, he should still be called a Vampire. The only thing is he is in a league of his own due to it's origins, and the fact that he is not JUST a Vampire, but a powerful Sorcerer and Alchemist, strong enough to raise a supernatural magical fortress for himself, that crumbles upon his death, control and summon legions of the undead and demons, and has become bound to the force of Chaos, which fuels his power.
He's not JUST a Vampire, certainly no ORDINARY Vampire, but he is STILL a Vampire nonetheless, and Alucard inherited half of his Vampiric genetic code, and seemingly some of his magical ability as well- the ability to steal souls seems to have become an essential part of Dracula's being, of his very soul, with or without the Crimson Stone, An ability passed down somewhat to Alucard, (SOUL STEAL!) and inherited by his Human reincarnation Soma.