If a vampire's heart is just some dead organ that doesn't do shyte, then the most popular lore method of killing them by staking them through the heart wouldn't do bugger all to a vampire, would it?
In virtually all depictions of them, an active vampire's heart does beat. Whether it's Blade, Buffy or Bram Stoker's, when a vampire suffers dismemberment, there's massive blood spray. Blood spray is caused by a beating heart pumping blood through arteries that are now severed. If it wasn't pumping blood through the system, there'd be no blood or at most some drip from the end that's pointing downward through gravity (i.e. no blood coming "up" from the neck in a decapitation).
In some media it's even directly shown e.g. In the Underworld franchise, when the hibernating vampires (Victor and Marcus) are revived, the heart was directly shown to start beating again as blood started to enter their system. A beating heart was also shown when Selene reached in and brought David back to life.
Regardless, this is madmate's "universe" and he can make whatever "vampire rules" he likes, IMO, and that would appear to include blood flow to the D.
Eh, like I mentioned before, it's all dependent on where you get your lore from. A simple google search asking "Do vampires have a pulse" will straight up tell you this:
"According to vampiric legend, vampires have no pulse, no breath, do not eat and are for all intents and purposes dead."
And if you have no pulse, you have no blood pumping through your system, thus, no heartbeat. And of course movies are going to have blood spray and show a beating heart, cause it's movies lol. It needs to be dramatic and over the top. And Buffy's vampires didn't have a heartbeat (again, you can just quick google search that). They did explode into dust when they were staked though, not spray blood.
In Twilight and stuff like Vampire Diaries, the vampires are said to have beating hearts... I hope that's not what you are basing this off of lol.
As for the stake, again all depends on the lore you believe in. Some stories tell of stakes only stunning a vampire, immobilizing them, not actually killing them though. Then of course, the classic TV version where a stake kills a vampire (unless you're going off the Buffy movie, where a stake just made him groan for a long period of time lol).
But yeah, in the end, it's whatever you want it to be. It's all fiction, none of it is real, so go with whatever you want!