As far as remakes go, this game fills all the checkpoints. Fuzzy controls keep it from being great.
Before we begin, let's define our expectations for a remake. 1) It must remind us of the original in as many ways as possible. 2) It must update graphics/music sufficiently to not be an eye/ear-sore. 3) Any additions/changes to the game should be used sparingly, and only to "fix" problems from the original.
There are, of course, other aspects of reviewing a game, but these 3 are things that should additionally be kept in mind since the original review score of the game is our starting point.
The original Ducktales would have received a 9, in my opinion, and that will be our starting point:
1) Reminiscence of original: This game makes excellent use of the original gameplay mechanics and characters. The joy of platforming across varied terrain via pogostick, and collecting as much money as possible in each level is not reduced in any way. The death mechanic is kept, in that losing all your lives in a level results in having to replay the level from the start (making the last level more difficult, indeed). Using original actor voices is also a huge plus, as anything less would have felt like a cheap imitation (like song covers in guitar hero games). For these reasons, the remake maintains a 9.
2) Updated graphics/music: The graphics are very pleasing, as the backgrounds are diverse and colorful, and enemies/characters move fluidly through their animations. The music is also pleasing, especially the background music for the Moon level. Altogether, Ducktales: Remastered hits all right notes for updating music and graphics, and the game maintains a 9.
3) Additions/changes: In case you thought I was going to just give the game glowing review, here is where that changes. WayForward decided to add in cutscenes all over the place to basically explain/embellish the original story. This, by itself, is not a bad thing, as we get to hear (original actors!) from many characters from the show. However, rather than making the cutscenes immediately skip-able by the press of a button, they require you to press start, then select you want to skip, then press X. Combined with having 2-3 consecutive cutscenes at the start of each level means a lot of button-pressing just to play the game. This annoyance is only further magnified by how easy it is to die and start all over again (especially on harder difficulties).
Another change is in the fuzziness of the controls. Hit zones seem arbitrarily expanded around spikes and enemies, and the stickiness of movement doesn't help this at all. The pogostick mechanic is also somewhat wonky, as pressing the pogo button doesn't always seem to work. In a game as punishing for dying as this one, receiving damage at random points make it frustrating. For these reasons, I drop my score to 7.
Other things:
The game maintains the fun factor of the original, though by slightly modifying the approach. Finding hidden gems is not as much fun because having a minimap makes exploring much easier. But to counter this, collecting gems has real value in unlocking art and music (previously, money collected was basically just your high score). Overall, I don't think WayForward put out a terrible attempt at a remake just to make easy money. The only part where they failed was the inexact controls and tiring cutscenes, but I think we can look past these issues (well, it cost them a couple of my review points) for a $15 remake. Finally, if you liked/loved the original, you will be happy to play this one. Nostalgia is a fickle mistress... on the one hand, you will be happy to pogo around and hear original character voices. On the other, random damage and punishing death mechanics will give you the urge to rage quit.
Update: A couple of things regarding some negatives of the game from other reviewers. The mini-map is not available on Hard mode and above, so complaints about not being able to "discover things on your own" are only a problem if you forego the extra difficulty. Additionally, Extreme mode goes even further, and forces you to use the traditional pogo jump (must press the pogo button AND down on the control stick), along with no checkpoints, at all.