The combat cross is the vampire killer. I think Zobek narrates it somewhere in Chapter 5. Yes, it's stated in this game, which is currently a different universe (a reboot of the series, which means unconnected to other CV games) than the previous games.
It's not a whip though. No more than any other random length of chain in any case. You use it as if it were a whip, but stabbing someone with a pencil doesn't make that pencil a sword.
Besides, this isn't even about whether the Combat Cross is a whip or not, it's about whether it's the Vampire Killer or not.
use a different analogy that one doesn't work as the act of stabbing is not sword specific. also if a chain isn't a whip tell that to konami because the original castlevania games had simon use a chain with a hilt and s spiked ball at the end and called that a whip