I read that everything in an Elder Scrolls is, in some way or another, canon. So technically the Dragonborn ended the Civil War, cured the Companions of LLycanthropy, helped Nocturnal, and assassinated Titus Mede II.

Without Titus Mede II I assume power in the Cyrodiilic Empire has:

A) Fallen to the Elder Council

or

Fallen to Mede's successor

But I don't think Mede has a successor, so technically no one's lit the Dragonfires...

So what's happening with all that, I don't know to much about it.

We don't know if Titus Medes II has a successor or not so we can't say it's the end of the empire because of that, another thing is lore-wise there is nothing stating the Dragonborn did all of those and just because the dragonfires don't need to be lit anymore does not mean a new emperor can't be crowned in. An emperor is a title for the leader of an empire, not some metaphysical position given by akatosh.

They weren't lit since the Oblivion crisis - the statue formed from Akatosh's avatar replaced them (also, they couldn't be lit without the Amulet of Kings - and that got shattered).

But without one they can't light the Dragonfires, right? So they're not lit right now? That's what I was wondering, as vague as I said it, heh.

Also after the Warp in the West, I think everyone assumes everything that happens in-game technically happens.

What Martin did in Oblivion meant the dragonfires never had to be re-lit ever again, Martin became the stone that keeps the barrier up to stop the Daedra from invading. The warp in the west is different, that was a dragon break, I suggest you read up on them.

I think TJ mentioned the Warp in the West to explain his insistence that everything that happens is canon; he is not suggesting that it has something to do with the Dragonfires.

That said, everyone else is right. The Dragonfires have not been lit since Martin's day (more accurately, since Uriel VII was assassinated). The Medes are not Dragonborn Emperors, as far as we know, and the purpose behind having Dragonborn Emperors in the first place was to reinforce the Covenant with Akatosh (which is the reason why the Dragonfires were so important); the Covenant ended with Martin and the shattering of the Amulet of Kings, so there's no need for Dragonborns on the throne.

Cyrodiil got them a fancy new statue. They had to add a few stories on to the Temple of the One to house it. It's a real beauty, and you can feel a sort of hum if you put your hands on it. That's the new Covenant. No gems or fires required.