Gameplay: Shadowgate is not reinventing any wheels here - it plays exactly like its predecessor and exactly like any other point-and-click adventure game, a set of pre-defined commands used to interact with the world and solve hella puzzles. The game deftly avoids making you actually pixel-hunt, most interactable items fairly easy to spot.
The game is an adventure of the old-school, with red herrings everywhere and huge amount of items you can grab that you will never actually use. Nearly every puzzle has good, if sometimes somewhat obtuse hints, with very little ♥♥♥-pull adventure logic. The difficulty levels are also very serious, massively simplifying things on the easiest level as compared to the hardest. You /can/, on all difficulties, screw yourself into an unwinnable position - the game will allow you to destroy necessary items (though not casually) and it's extremely possible to just run out of time (though not very likely).
The biggest flaw in the gameplay is some UI related clumsiness, as using items on the environment can get very clunky very quickly when you're experimenting on a puzzle. Items can be bound to number keys for things you use a lot, but I don't think that ended up particularly useful near the end.
Story: Shadowgate has never, on its own, had a particularly deep mythology. The Shadowgate remake drops a lot more lore on you, completely resetting the world and freely changing some very major details. It does some interesting things once you get to the end.
I did personally find it to largely suffer from being written by 50-year old men whose greatest influences are clearly in the Lord of the Rings vein, naming conventions clearly suffering from a lack of... I want to say modern creativity. It's all a bit out of date.
Art: Here's where Shadowgate really shines - which is important, since the game is little more than a series of paintings you flail at with a mouse. Shadowgate is not a colorful place, with most scenes generally only having two or three different colors at any time, and Chris Cold does an excellent job making a dreary Shadowgate that seriously looks like it wants to kill you.
Jair in particular is excellently rendered - the classic portrayal of the game's protagonist was a standard square-jawed manly hero in full armor and a beautiful head of hair. New Shadowgate portrays Jair as a man dragged out of his life and sent on a journey without ever really being allowed to understand why - his hair is long and filthy, his cloak is tattered, and his shadowed face imparts the idea that Shadowgate is destroying him even as he triumphs over it.
Perhaps most importantly, the art is /clear./ Despite everything being dirty, dull, and cracked, mostly in greys and browns, nothing looks maddeningly ambiguous. An item on the ground is clearly an item on the ground, a doorway is clearly a doorway, and if you at any point get fooled it's because the game is actively trying to fool you.
Music: I have a clear bias here - New Shadowgate's score is an orchestral treatment of the original music, the old songs appearing as almost etherial strains inside some deeply atmospheric stuff. Compared to the original, this score is much darker, much more ominous, and much more effective (which shouldn't be too difficult, considering the original was on an 8-bit system). There is an appreciated option to set the music to the classic beeply bops.
Shadowgate: Yeah, it's Shadowgate. You can die on almost every screen, you watch your torches steadily dwindle down, and the Warlock Lord pops in from time to time just to talk ♥♥♥♥. Most sadistically, the game is explicitly /not/ the previous Shadowgate. Very few puzzles are solved the same way, and the game will often directly punish you for having the unmitigated gall to underestimate it in this fashion. Much like the original, the game (on Master difficulty) is not here to be your friend. It is here to laugh at you as you stare blankly at its legitimately hard puzzles and then brutally kill you for blinking.
All told, I give the game high marks. The UI's clunkiness just takes a little getting used to, and if you enjoy adventure games that kind of slap you around, you can't get much more slappy than this. If you're a fan of the original and you haven't picked this up yet, you should absolutely do so.