I find it funny that you can find Defcon in that list where you kill millions of people yet has the ESRB rating: "TEEN with Mild Violence. PEGI Rating: 7+".

That is kind of funny. I guess they don't have "Implied massive global genocide" as a content descriptor...

"The death of one man is rated M. The death of millions is rated Teen."

As mentioned before, many adventure games fit your bill. Some of them may feature one or two occasions where you may need to harm someone in some way, but that's never the be-all end-all objective or main form of interaction.
Some gog specific adventure games: Broken Age, Tales of Monkey Island, Sam & Max (features some comedic violence on the part of the bunny, but that's not the main focus), King's Quest 4, 5, 6, Legend of Kyrandia games, Book of Unwritten Tales, To the Moon and Simon the Sorcerer 1 and 2.

Some non-adventure games that do not feature violence as the main objective: Papers Please, Stacking,

There are plenty of games that don't involve killings, but they differ wildly on genre. I think you should be slightly more specific on what kind of game you'd enjoy, you'll get better suggestions that way.

Many, many adventures have no killing, as do most puzzle games. Same for managerial/building simulations, as well as sports. Surely "no-killing" isn't the only criterion.

PC or PS3.

Its supposed to be possible to play consortium peacefully.

Most point-and-cilck adventure and puzzle games never center around death, though some may have violent themes (e.g. Sam & Max).

Stuff like Pac-man Adventures (SNES) has you almost literally poking and prodding Pac to move and do things. Puzzle games like Pieces (SNES) or board games like Carcasonne (also on Android/iOS) or Snakes (tons of variants) are completely devoid of violence and are instead focused on logic and reflexes.

On GOG.com, adventure games like King's Quest will have to occasional scenes of violence (animals getting hurt, monsters dying, and more often than not, YOU dying).
The MONKEY ISLAND games have small smatterings of violence (insult sword-fighting, slapstick comedy), and one major death (the main villain; repeatedly).
BACK to the FUTURE features mostly puzzles and races.
MYST and LIFELESS PLANET are about pure exploration.
LONG LIVE THE QUEEN, I think is low on violence -- (were there "dungeon sequences" where you had to go slay something?) -- but it's mostly a construction-type game where you are training the Queen-to-be. (Or in the case of OCTODAD, wanna-be-human.)
Similar games are Redshirt and Leisure Suit Larry, while both are non-confrontational, both are also filled with sexual situations.
Ditto with simulation games like CAPITALISM; technically no fighting, but mostly numbers-crunching and socio-/political stuff. Ditto with the fantasy equivalent: KING of DRAGON PASS. Less so is SimCity 2000 where you can actually see your city grow instead of reading reports.
How about the KYRANDIA games? Mostly about a student in the mystic arts, right?

Hard to think of an action game that isn't a sport (driving, soccer, etc.) kind of game.
For the PS2, even though it's about fighting, try looking at PENGEL: QUEST FOR COLOR. You literally draw shapes that charge and thrash about.

Or Rhythm Games like GITAROO MAN and SPACE CHANNEL 5. (Back in the day we would use controllers to dance instead of moving in front of a camera.)

Peggle and Peggle Nights, for sure.

Kerbal Space Program is a great one (Early Access right now -- very playable)

If it's for kids, the Humongous Games games (Putt-Putt is what my kids are playing)

You break illusions in Mickey Mouse and The Castle of Illusions. Some minor violence there.

On GOG: Among the Sleep (not a "safe" game, but you can't kill -- you're a 2-year-old child)

Most sports and racing games.

Someone mentioned portal 2. You don't try to kill things, but they try to kill you. There are guns in the game. You just don't wield any (except the Portal Gun, which is the best gun ever invented).

Wheel of Fortune and Jeopardy! are great.

Hotline Miami (kidding! ultra-violent)

Lots of adventure games like The Longest Journey, Space Quest, King's Quest (Quest for Glory does have action combat, so not that one).

There's some flight simulators without combat.

Port Royale has combat, but the objective isn't to use it. It's just there for self-defense (unless you want to play a pirate). I've only got PR3 and I've yet to get into any major combat and have enjoyed some good trading.

your post just made me realize how violent I tend to like my games... don't know what that says about me.
Anywho, people mentioned Myst, Thomas Was Alone. I've played those and both are fun. Journey is supposed to be super fun, it's a game i've been wanting to play and is non-violent.

Great suggestions, I'll say Q.U.B.E., Restaurant Empire games, Kami, Zen Bound 2, and many racing games.

Will expand as I think of more.

I haven't got a suggestion for a game, but I received this from a buddy just moments ago via e-mail and when I saw the title of this thread I felt I had to share it:

"It's only when a mosquito lands on your testicles, that you realize there is always a way to solve problems without using violence."

Nope. There's that terrible section that involves killing 'zombies'.

A few games that I've played and enjoyed recently:

Race the Sun
Farsh
Super Splatters

Anyway, there's way too many to mention - just look towards puzzle games, adventure games, simulators, racing/sports games, anything with an abstract art style.

Pushover is nonviolent but it's quite tough.

Any FIFA or Pro Evolution Soccer game, provided you don't choose Spain as your team. If you choose Spain, your players might get savagely raped by the opponents.