When playing Edgar Markov, what is the definition of a "Vampire spell"?
A Vampire spell (for the purpose of Edgar Markov) is a spell which has the Vampire (sub)type; its name doesn't matter. You can find the type(s) in the bar between the picture and the rules text. Vampire Cutthroat is a "Creature - Vampire Rogue", so it counts; Mark of the Vampire is an "Enchantment - Aura", so it doesn't count.

There are no non-creature spells which explicitly have the Vampire subtype, as this Gatherer search shows. There are non-creature spells which have all creature types thanks to the Changeling ability, such as Crib Swap; this search lists all 6 of them.