I assume that "vampiris" is a pseudo Latin 3rd declension i- stem noun (eg. civis) for "vampirism". But how does "sanguinare" fit in?

"Sanguinare" could be the infinitive of the verb "bleeding", but I don't see how an infinitive could be used this way.

The next closest word I can find is "sanguinarius (blood thirsty)", but then the nominative would be "Sanguinarius Vampiris".

I know that "Porphyric Hemophilia", the kind of vampirism in Morrowind and Cyrodiil, is not exactly Greek or Latin, but an English term with Greek word roots. Maybe "sanguinare vampiris" is also such a name? But I don't see how it fit in English morphology either.

How exactly was the term "sanguinare vampiris" formed?