Well, there is the whole part about story and quests. All this is implemented using a scripting language also used for the npc dialogs. This includes controlling NPC moods, gaining/loosing quest items, setting/checking quest flags etc. Pretty much most of the actual game play - besides combat.
Well, I believe the Unity engine has a pretty sophisticated scripting aspect, though I've never actually tried it. It's supposed to work with languages like C# - which would enable even a complete amateur like myself to make most of the code needed for the things you mention.
Then there is the level setup which is implemented using a fairly elaborate "trigger/trap" system. This system implements all the puzzles (levers/buttons), text messages, key/lock gameplay, environment transforming (for example: drain the water puzzle in UW1), special camera angles, special graphics.. and much more!
This is another thing I expect is fully possible with the Unity engine, with proper understanding. It's certainly not an easy thing - but very doable for a dedicated team.
Then there are all the items. Which monsters drop what? What does the individual items do? What about magical items? Spells?
All those things are just variations of the basic challenge of making scripting work with the engine. As soon as you grasp how the Unity engine works with scripting, you'd be able to overcome all these things relatively easy with an object-oriented language like C#.
It would take a lot of work, obviously, but the technical "coding" challenge is not insurmountable.
IMO there really isn't any "easy" way. If you decide to reverse engineer the original file formats, then you gain a lot of "implemented game play" each time you manage to decode one more piece of the files - but decoding it all is *hard*.
If you go for the "lets just reimplement it from scratch" approach then you'll quickly realize just how much data is needed for this game
I never said it would be easy.
But to reverse-engineer and re-use assets, means you'll get a game looking only marginally better - and then I personally think it's a huge waste of time. Then I could just go play the old game, and deal with the weaknesses.
Once you're "into" 3D development, a game like Ultima Underworld is a breeze for the professional - because we're talking relatively simple assets. You wouldn't need a zillion cutscenes or high-level animations, or other things that require vast production values.
You need a handful of 3D models, and a pretty limited set of textures - and the rest is scripting and recreating levels using a powerful editor. Sounds can probably be re-used for the proper nostalgic feeling, and 2D art for portraits etc.
As I said, a HUGE undertaking for people not inclined for development, but for a professional team - it'd be a very doable thing, and I bet they could make it all work within 6 months.
But no one will do that, because they'd rather focus on profit.