The little dolphin who cried...

Tough question- most sidescroller games opt for a more pixel-influenced style.
Aquaria might fit the bill, though. Great game with great art.

Thank you...you...u...

Rain Blood Chronicles: Mirage and BloodRayne Betrayal might meet your criteria.

Dolphin's cry.

thx

Well, it's a side-scrolling Platformer with great art: http://store.steampowered.com/app/237630/

thx

Bump!

Not really similar, but Ori and Child of Light have beautiful art. Apotheon also has a very interesting art style. The Cave looks good too.

The Bridge maybe?

Maybe Valdis Story: Abyssal City fits your bill. You can buy and play it and then give your opinion. I'm still not sure it it interests me enough. The achievements sound partially painful.

Vessel has a similar art style but I see you've already played it.
Closure has a quite unique style but I guess it's different from what you're looking for.
Sideway(?) has an interesting art style but controls are not that good.
A.R.E.S.(?)
Dustforce(?)
Mechanic Escape(?)

Chronology has a somewhat similar style to Teslagrad. The other games I can think of at the moment are already mentioned.

I remember playing the dolphin game long ago on the game cube, was kinda creepy

I'm not sure, but I thought you should see this.

Sailor Mouth~

I haven't played any of those games you listed but if you're looking for a 2D platformer you can't go wrong with
Rayman Origins or Rayman Legends.
I own them both on console but according to reviews the PC versions seem pretty good as well.
I personally prefer Origins because I felt like I had more enjoyment out of it(was more challenging and almost every level was as fun as the other) but really it's fine to start with either one of them. ^^

hand-drawn or whatever it is called

Cel-shaded is the term you're looking for, me thinks?

Unfortunately it doesn't seem to be used much on Steam.

I'm struggling to think of anything relevant, but have a happy cake day bump!

bumpity