As I understand it: kinesthetic 2d platformers are games with a flowing movement, where the player jumps and wall-glides a lot. This is as opposite to more mechanical games where the player mostly has both feet on the ground, like ABUSE.

Dustforce DX ... haven't played it yet, but bought it solely for its movements.
Downwell -- pretty fun, actually!

Underwater games has some nice flowy movement, even if they can't exactly be called platformers:
Aquaria
The Aquatic Adventure of the Last Human

Limbo -- a slower pace, but real good movement here!

They Bleed Pixels -- not on GoG, but pretty damn good!

A few I think are pretty good/excellent (all have a 4 star or better rating) and I have in my collection here on GOG that have not been mentioned yet:

Magicmaker
Giana Sisters Rise of the Overlord (I know people said the series, but this is one on GOG not specifically mentioned yet).
Volgarr the Viking
Rogue Legacy
Valdis Story: Abyssal City
Hocus Pocus A little old school.
Shantae Risky's Revenge
Mark of the Ninja

As others have pointed out Guacamelee! is a superb sidescrolling Metroid/vania action platformer. Unless you're going for some of the hidden rewards it is not difficult but does require a controller and is loads of fun. The screenshots don't really do the aesthetic and colors justice. It's one of the most visually impressive indie games I've ever played.

Broforce another Indie I picked up last weekend and couldn't put down until I finished it is equally great. Before I played it I thought it was simply some 8bit retro version of Contra with some stupidity thrown in for a laugh. What it actually is, is a satire of American jingoism and action movies that is genuinely funny, with engaging gameplay via its sidescrolling exploration and action. Also a game best suited for controllers.

Both of these titles were immensely enjoyable and will likely stay with anyone that plays them.

A couple other ideas, if you're the type of player who loves it when the game punishes you for doing something reasonable by killing you in silly ways.

Syoban Action: Freeware game (with an open source version) where you play as a cat and which feels like a parody of Mario. Game is filled with traps (think hidden block traps in Mario hacks/Mario Maker levels, but more varied) which will kill you if you don't know about them (or just forget). My favorite part is the end of level puzzles; it is possible to die after hitting the flagpole. Fortunately, the game doesn't end when you lose all your lives, so you effectively have infinite lives (which is a good thing).

Eryi's Action: Imagine Syoban Action if it were a commercially released game, and you get Eryi's Action. From what I played, I liked the art style and the music. One difference is that you can grab various things and throw them, adding a bit more of a puzzle element. Also, this game is even sillier when it comes to deaths (one time when I died at a point that I was expecting to be safe had me laughing for quit a while). Also, while Syoban Action had a gentle introduction, Eryi's Action starts with the death traps right away. Not on GOG, but the game is supposedly DRM-free if you buy it from the publisher's website, plus there's a free 2 level demo available. (Note that I have only played the demo, and only played up to the start of the second level.) Lives are handled like in Syoban Action.

There are a few others, like I Wanna be the Guy (and its thousands of fangames of varying quality), and Owata (online game that requires Flash Player (I recommend using a VM for this for security reasons) and was one of the earliest examples of this sort of game).

Well, even if I admit that there are some hard jumps (which get *pretty crazy* by the end xD), you can set custom checkpoints whenever you feel like it. If my chaotic memory isn't playing tricks on me, there's a mode with no death limit, so you can really just enjoy the game by setting the checkpoint prior to a hard part and just try without losing much. It's pretty challenging, but a totally doable experience.

I got this as a side game in some random bundle, but I haven't since played a better named game :D

The game itself is nice, but if I recall correctly, it has no save function, so you have to play it in one sitting. I take it it's pretty short, maybe an hour or two at max, but still, IMO games like these need to offer players the option to take a break before they lose their sanity. Checkpoints alone don't necessarily help with that. ;P

(Truth be told though, I think almost every game needs to offer that option, regardless of the difficulty, just so you don't lose all of your progress if anything comes up and you need to interrupt your gaming session.)

Bad kinesthetics in an otherwise good game... the best example I can give is 'Castlevania: Symphony Of The Night'. Whilst most people would say they enjoy the game, they enjoy the exploration, the RPG elements, the art direction and atmosphere, but almost no-one would list the level design and sense of flow as a reason for loving the game. In fact, you probably don't notice it unless you look for it; but if you replay 'Castlevania: SOTN' you can see just how little design has gone into the levels. Often rooms are flat and straight with practically no platforming at all. Sections often repeat with the same enemies facing you one after the other, or the same obstacle being repeated two or three times in a row.

Most platformers have good kinesthetics because it's often a focus of the genre. But hopefully that can explain what the difference is. I'd say one of the best examples of good kinesthetics is 'Super Meat Boy' but it's not on GoG. Any time you play a game and can describe the gameplay as 'fast', the controls as 'tight', and the challenge as 'hard but fair' you've probably got a case where the designers took special care to put good kinesthetics in game, to make the movement feel responsive and consistent, the controls fit what you expect when you use them, and the level design complement the characters abilities.

I've played a lot more 2D platformers on console than PC. Ones I have played and enjoyed on PC are Freedom Planet, Rayman, Earthworm Jim, Cave Story, some Mario fan hacks/games, Volgarr the Viking, Odallus, Jazz Jackrabbit.

I've heard about Jazz Jackrabbit multiple times but I've never actually played it. Same with the Commander Keen games, I know of them but never played them. I hear they're both well know PC platforming mascots but somehow I've passed over them every time.

One PC specific game I have played is 'New Super Marisa Land' which is a Mario clone with anime girls from some shmup franchise I think. It's actually shockingly really good though. Though it is entirely in Japanese so it does help to be able to read Japanese.

IMO that's more of a design choice, rather than difficulty. In these short-toenjoy long-tomaster arcade kind of games, I kind of prefer the lack of saving, so you can have your little blasts of fun without worries, but have to commit a little to actually finish the game.
Totally subjective though. I recall people seriously arguing over that with Volgarr the Viking :P

But at least the checkpoint system makes you less prone to ragequit. I have almost broken my controller playing Super Meat Boy, They Bleed Pixels and IWBTG, even if the restart stages aren't that far away from each other.

N++

I know, I didn't mean to say it makes the game more difficult, but it makes people less likely to play it due to worse ease-of-use. You said "little blasts of fun without worries" but to me dedicating an hour would not be a "little" blast of fun, and having to commit to that no matter what happens or being punished with losing all your progress wouldn't be "without worries". I guess everyone draws the line at a different time, but for me the game is already too long to play without break or replay it from scratch. And I'm not even a very social or hardworking guy or a parent, as other players might be. I still can't predict if I have time and energy enough to play through a game like that in one sitting. ;)

But yeah, it's pretty much subjective whether that's an issue or not. Just saying it seriously reduces your target audience if you make that design choice.

I've actually found I've rediscovered the joy of pick-up-and-play gameplay since trying to get the Platinum Trophy in 'Shovel Knight' on the PS Vita. It's changed how I play because I'm going for specific trophies, I'm trying to get the "no death run" trophy and the "smash all checkpoints" trophy. This means every level needs to be done perfectly, if I die, I switch off the game entirely and come back to it later. I only ever do a single level, and that means around 15 mins of gaming at most, probably closer to 10 mins. I know these levels can be speed-run in around 4 mins each because I've seen people do it on YouTube.

This new approach to how I'm playing the game, in order to get these trophies, has changed my perception of the game quite dramatically. This is what good trophies/achievements should do I suppose, they change how you play the game and make the game feel new and different just because of the way you're playing it. In that regard it's been a huge success.

One title that seem to stand out is Elliot Quest.

Yet to play it, though 2D platformers i can eventually recommend are :

Eversion : i forget most of it, been years but it has some reputation
Spoiler Alert : Funny game it plays in reverse
LaserCat : cute, fun & minimalist

I never played Symphony Of The Night, so I can't comment on it, but I think heard that the level design was actually great. Once you realize that, SPOILERS, in the second part of the game the castle is inverted? At that's what I think I remember about it... Was that a different Castlevania game?