I've played every incarnation of D&D since 1977, DMing most of the time. I knew Gygax slightly, and introduced him to Bioware's Neverwinter Nights game, which, I think is the best D&D game brought to computer to date. I'm a computer gaming conceptual artist and writer, as well as a comic artist with Disney with some 30 years of experience.
I'll add my two coppers to the mix on what Larian seems to bring to the world of D&D.
Pen and paper campaigns largely happen in one's imagination. While there are rules governing the chances of doing this or that, quite a lot is very much an abstraction of the real world's rules about gravity, time, and space. It's physics with a fantasy/medieval theme. You listen at doors. You sneak about or run like hell. you fall to your doom or cheat gravity with a Featherfall. But, it's based on what we know about the real world. When one tries to bring a pen and paper game to a computer, what you are really doing is taking our real world physics and showing them on the screen, instead of abstracting what is happening inside your head. So, there is a real challenge in portraying cover, height advantages, slippery surfaces- all the stuff we know in the world.
My point here is that the fantasy stuff comes from the rulebooks- the monsters, player classes, etc. The world itself is really based on our own world.
As computers have progressed, we've gotten to the point where it's easier and easier to portray the world we live in more accurately. Back in Baldur's Gate I and Ii, there were a lot more limitations, obviously, as to what you could try and show or simulate.
The biggest differences between now and then are how it is possible to allow players to use ground, cover, facing, and stuff lying around to your advantage, (or detriment in the hands of the enemy). This in turn allows for greater tactical thinking, deeper strategy and more involving and realistic combat.
I personally think Larian is quite wonderful in the way they tackle encounter design. Smarter players who are willing to stop and think before acting are usually rewarded by using cover/high ground and whatever is laying around handy. Warrior characters have to be very mindful of their feet, while magic uses generally are rewarded if they carry teleporting type spells that allow them to avoid trouble and control the ground they find themselves on. It seems to me Larian has slightly "helped" the warrior classes because of the nature of their need to traverse hostile ground more than the ranged classes need to. Which, is just smart. This sort of problem doesn't happen often in the more abstract pen and paper world.
These tactical needs dictate play design in a lot of ways. BG III's environments are a lot more complex and unpredictable in ways that a pen and paper game under a DM are not. The players and monsters can cause all sorts of cascading events by tossing, jumping, climbing, teleporting, pushing, poisoning, burning, shocking, wetting, and Lolth knows what.
When a player does this in a pen and paper campaign, you don't get the same rippling effects in an area with the same depth of detail, no matter how good your DM is, or how imaginative the players are, on a regular basis. In BG III, in a big battle, all manner of shit is going down at once, (well, in turns that represent at once, anyways).
So, I think, that the crux of the matter of "how close" BG III's "rules" are to 5th edition really is a lot more problematic than the mere numbers involved in AC and hit points, or the nature of thieves jumping behind some monster who has 3 backs. Larian needs to do what works in order to provide the most immersive, deep, real world feeling experience that also "feels like" a night of D&D using the latest ruleset.
It's gotta be a daunting task.
I personally find myself being drawn back again and again to try different classes and experiment with different approaches. I find myself quite excited to try a Bard. I REALLY want to see as many classes and races as possible, and dabble in extremely useless and probably doomed multiclassing.
In short, this is as much fun as I've had with a computer D&D attempt since Neverwinter Nights, and this is just early days.
This one is going to keep me up nights for a long, long time to come. I dig it. These guys know what they are doing, in my spellbook, anyways.