Note: the only demo available for Dark Souls III was an off-TV presentation that a Bandai Namco representative walked us through. As such, this article will be split into two parts - what I saw and what I thought.
What I Saw:
Dark Souls III definitely looks closer to Dark Souls thematically, though there are some aspects similar to Dark Souls II as well. One part of the presentation focused on a dragon spitting fire across a bridge (some things never change, I suppose), though this portion was also used to showcase a renewed focus on utilizing the environment to defend yourself against enemies (a la the arrow traps in Sen's Fortress).
Two boss fights were shown off (I'm assuming two, since the HUD was turned off for the presentation—a feature that will be available in the retail release, apparently.) During the second boss fight against some sort of dancing zombie skeleton (it's hard to explain, but trust me when I say it's way cooler then it sounds), it was shown that boss mechanics from Bloodborne (where a boss might change its attacks halfway or a third of the way through the fight) will be much more common than in prior Souls games. Also during this fight, it's shown that attacks that bosses do might affect the environment in unique ways—for the dancer bossfight, its fire sword can cause the ground and some pillars to catch fire.
What I Thought:
The new mechanics certainly seem interesting, and the focus on the environment being both a tool and a danger is a change that I'm definitely intrigued by. Miyazaki-san explained the change as a means of making the difficulty "fair," although Dark Souls III aims to be harder than the previous titles. One example that wasn't really talked about, but I noticed, was that one of the enemies that ambushed the person playing the demo could be anticipated due to a blood splatter on the floor to the side of the door.
The new stance mechanics add some additional attacks to weapons, and from what was shown, it seems that every weapon will benefit from these new stances. Enemies, as well, seem to have received an upgrade—and both the player and enemy mobs have received a boost in speed. Both of the new bosses are especially interesting - one of them was an abyss-like black blob that attacked like a giant rat, and the aforementioned dancer had some attacks highly similar to some new attacks that were shown with the dual scimitars. One particular attack—a prolonged spin attack—was especially brutal and unlike anything I've personally seen in a Souls game to date.
To round it off, the new Tombstone mechanics seem interesting and will allow for more lore to be littered around the world, adding some more flavor text for each area in the game. There's not much to be said about the other features, but the new particle effects seem nice, albeit slightly understated. Overall, Dark Souls III looks like another great entry in the series, and I'm eager to learn more in the coming months.