Another recommendation that I haven't seen here is "A short hike"
https://steamproxy.net/steamstore/app/1055540/A_Short_Hike/

Wonderful little game of discovery and exploration

A few games that I don't think have been mentioned yet:

OPUS: The Day we found Earth: you search and scan stars while looking through a telescope looking for Earth in an attempt to get back home.

And from the same people:
OPUS: Rocket of Whispers: you scavenge the ruins of your hometown for materials to build a rocket capable of reaching space to send the ghosts of everyone who died in a plague (including everyone you knew) into space so that they can finally rest in peace.

These two are part of the very short list of games that managed to bring me to tears.
They are simple and short but absolutely beautiful and I highly recommend them.I played them on Switch but they're also on Steam and mobile.

Lastly,
Monster Prom: an up to 4 player coop dating sim where you try to charm your monster classmates into going to prom with you. Nearly every single one of the romance options is some kind of sociopath and the game is hilarious, especially when played with friends.

Spoilers for Inside Near the end of the game you gain control of a giant blob of human flesh that then starts running down scientist. While it isn't traditional combat mechanics, it is still very gruesome. So I'm not sure if it belongs on this list.

All the non-combat games I have in my library that I enjoy.

Life is strange
Portal 1 & 2
Rocket League
Super Mega Baseball: Extra Innings
Orwell
Dreamfall: The Longest Journey
Cities: Skylines
F1 2015
Alchemy Mysteries: Prague Legends
Chains
Emily is Away
Firewatch
The Awesome Adventures Of Captain Spirit
Else Heart.Break()
The Longest Journey
Limbo

Hey, check this one:
https://steamproxy.net/steamstore/app/888630/Another_Sight/

Add https://steamproxy.net/steamstore/app/837470/Untitled_Goose_Game/!

I would like to recommend Eco. It focuses on consequence and unity of decisions, of including every person in a discussion, as all decisions have consequences, and this game aims to make you ALL work as one.
Also, don't take my name too seriously, there is a long story behind it that is ultimately mocking the ideals that were preyed on to convince me to enlist many years ago:

http://steamproxy.net/steamstore/app/382310/Eco/

I'm just going to add my two cents and list all of my favourites:

Other
Oxygen Not Included (build base, survive, barely there avoidable combat),
The Sexy Brutale (manipulate time to stop murders),
Stardew Valley (farm, fish, build, create your own goal, story),
Slime Rancher (keep animals(slimes), farm, explore, some puzzles).

I'm just going to add my two cents and list all of my favourites:

Puzzle/logic games
Antichamber (mindblowing puzzle game, illusions, will warp your mind),
The Bridge (M.C. Escher-style puzzle game, calm and nice),
Gravity Ghost (solve 2D physics puzzles, get story),
Grow Home & Grow Up (two games, same thing, explore and collect in 3D),
Human Resource Machine (programming logic puzzles, starts easy, gets very tricky),
World of Goo (pysics puzzle game, build, get from A to B).

I'm just going to add my two cents and list all of my favourites:

Pure story/experience focused:
The Beginner's Guide (essay on games in game form, emotional story),
Botanicula (cute and visually interesting point and click adventure),
Everything (philosophical exploration of the universe),
Little Inferno (burn things, burn more things, occasionally morbid),
The Vanishing of Ethan Carter (figure out a story, some puzzles, does involve murder).

I'm surprised to not see Thomas was Alone recommended on here, or The Talos Principle. I'm also a fan of Democracy 3 and Qbeh-1 as well as most of the Myst games.

We'd love to see our game here: Death Squared. Even though the name sounds like combat it's a co-op puzzle game

Here's a few off my game list: Oxenfree , Dream Daddy: A Dad Dating Simulator, "Papers, please" ,Tabletop simulator, Super Hexagon, Tales Runner, TIMEframe, Potatoman Seeks The Troof, Transformice, Bendy and the Ink Machine and The Lion's Song.

Cities: Skylines is another good one I don't think is in the list