Vampires is a deck that uses it's Main Deck as a toolbox unlike most decks which mainly use the ED as their toolbox.
The reason why it's okay to play so many one ofs is because there are more than enough ways to search the pieces.
Solitaire can special summon Uni-Zombie which can either mill Familiar or Retainer which essentially means that you can very easily search any Vampire Spell/Trap or Monster.
The biggest problem this deck has is that each time you summon one of the smaller vampires from the GY you lose cards so you need a critical amount of Vampire cards in your starting hand. Vampire Ghost as an example is a very strong card however you need more Vampire monsters for it to even work + any disruption will often stop you right in your tracks.
The going 2nd cards E-Con and Change of Heart work in a very unique way in Vampires because their rank 6 and rank 8 can just use your opponents monsters as if they were the correct level to summon them and those 2 + your Link monsters are going to be your win condition because they enable OTKs
The Synchros are just another toolbox that can come up from time to time but they obv aren't the main focus of the deck, the focus is stealing your opponents monsters and use it to make XYZ and Links.
Update:
Delta of Invitation is a Zombie support card that has been released after the posting my initial list.
It is a crazy card for Zombies in general and this also remains true for Vampires.
The most obvious change is that the Eldlich line now allows to actually set up a better board turn 1.
In my testing I was not only able to put up more Link Material but even Synchro plays got easier especially with Gozuki.
There have been also some minor alterations to the deck but Delta of Invitation is the one that had the most Impact during play testing