Mathias became a Vampire through the absorption of Walter's soul. He was "reborn" as a Vampire.
What sets him apart from most however, is that he was not sired. He had no master. Joachim was sired by Walter. Walter is technically his master. (Though given he rebelled against Walter and holds contempt for him, LoI doesnt quite follow the traditionalities of the matter of Master and ...spawn. (I cant remember the other term...) )
And Walter himself most likely was Sired by someone else whenever long ago. Mathias however, has no master- has no creator- His vampirism came to him through alchemy, through STEALING the vampirism from a Vampire, through stealing his soul.
It's kinda what bugged me about that little miniseries on youtube- Even in the original Novel, and the Coppola film, Dracula was never sired. He was always made a Vampire on his own. Be it by a supernatural will to live and refusal to die, or through um, drinking the blood from a bleeding cross.
Actually, thats another thing I notice- In doing what LoI did, it pretty much kept that intact. Dracula obtaining his vampirism through means OTHER than being sired by a Vampire.
(LoS is where they kinda went the other way. Although maybe it could be half and half, considering he absorbed Laura's Blood completely? So he went straight to final form and skipped the whole chain, going from Human to master all in one go, killing off his 'donor'?)
But I digress- Alucard is a Dhampir. he was born BEFORE CV3, while Mathias was Dracula Vlad Tepes and remarried to Lisa. if Alucard his Half vampire, it means Dracula himself IS a Vampire. Besides, he can still be a sorceror and a vampire, cant he? Not like it contradicts CV3's intro. it describes him as such, but doesnt explicitly say he is NOT a Vampire.