Properly, he should only be incapacitated, because according to established lore, the Old Gods cannot be properly killed because of how deeply they've ingrained themselves into the very structure of Azeroth. After all, Yogg-Saron's entire body spans at least from Icecrown to Grizzly Hills and from Storm Peaks to Howling Fjord, if not further, and who knows how deep. C'Thun's body spans the entire southern half of Kalimdor. If we actually killed these things, imagine what would happen once their bodies decayed and these big hollow spots suddenly appeared in Azeroth's crust (and possibly mantle and core). It was partially for this reason that the Titans only imprisoned them or put them to sleep.

Unfortunately, with the way the boss fights against these Old Gods have been constructed, it's put the adherence to that lore into serious question. We appear to kill them, but doing that should've already caused Azeroth to partially implode. A "Cataclysm" of sorts should've already happened when half of Kalimdor became a massive sinkhole. Some people speculate that none of this was ever the case, and that the only reason the Titans couldn't kill the Old Gods was that they weren't small enough to slip inside them and scramble their organs like we can (and have), but I don't buy it. If there was a way for the Titans to kill the Old Gods without completely destroying the planet, they would've done it even if it meant wiping out the surface and all life on it to do so. They wouldn't have thrown up their hands in a panic while some tinier mortal meatbags did it for them. For one thing, if the Titan constructs we see around Northrend are any indication, it would not have been a problem for the Titans to create smaller constructs to go in and do the deed in our place, as we already see comparatively diminutive mockups of Titans as the keepers of Yogg-Saron's prison (Freya, Hodir, Loken, Tyr, etc.). For another, all the dialogue we get from Algalon and the various Titan constructs strongly implies that they don't give a damn about the worlds they cultivate beyond putting them in a neat, working order. They were ready to glass Azeroth at the slightest breach of Yogg-Saron's prison, and there was nothing stopping them from doing that beforehand. Wipe the planet, kill the Old Gods, drop new seed races on the surface, and move on. Simple.

Unless, of course, killing the Old Gods would've caused the entire planet to be destroyed. The Titans want to put order to the worlds they visit, not blow them apart or cause them to implode on themselves. If killing the Old Gods caused that to happen, then even the Titans would've been hard-pressed to do anything but lock them up and pray that nothing interfered with the prison cells. Considering all we know about the lore, that seems far more likely than them just waiting on creatures small enough to kill them from the inside-out.

As far as the game mechanics and how we seem to have "killed" Yogg-Saron and C'Thun, the way I look at it is that we've simply hobbled them. We see and injure one room-sized piece of creatures that are almost as big as CONTINENTS. Yes, we "scrambled Yogg-Saron's brain" and "scrambled C'Thun's stomach," but creatures that big? With bodies straight out of Lovecraft? Who's to say they have one brain and one stomach? Perhaps we clocked them good in a vital spot, but I highly doubt they're dead, or at least dead in a conventional sense. Considering Cho'Gall's trying to resurrect C'Thun in the comics, and that Old Gods seem to exist in multiple dimensions due to their involvement in the elemental plane and supposed involvement in the Emerald Dream, it's not hard to envision Yogg-Saron and C'Thun being shut out of this dimension temporarily while their bodies heal their wounds.

In short, I highly doubt Yogg-Saron and C'Thun are dead for good.