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CD Projekt Red is following the TaleWorlds model of video game release, which is to say that "Cyberpunk 2077" was announced at the dawn of existence and will be released shortly after the heat death of the universe. While we wait for the atoms that make up existence to gradually drift apart, resulting in an eventual eternal stillness, here's some games that are mercifully already released that will give you that awesome cyberpunk feel.
"Shadowrun Returns," "Shadowrun Dragonfall," and "Shadowrun Hong Kong"
This is just about as classic cyberpunk as you can get. These games are based off of the role playing game "Shadowrun," and were released by Harebrained Schemes starting in 2013. They remain some of the best examples of world building in the video game market. They are 2d isometric, which will make those of us that were gaming in the late 90's feel a twinge of pleasant nostalgia, and will offer a seemingly new and unique play style to those that are new to the CRPG way of doing things.
By keeping the perspective farther away from the player, you are able to fill in more details of the world with your mind. The game designers do a great job of supplementing their art direction with in game dialogue and text descriptions, making it feel like you're playing a game of Shadowrun right at the table.
I guess it should be said that there's a bit of a twist with Shadowrun. Not only is it set in a heartless, corporate run version of our world; it also heavily embraces magic, monsters, and other elements from Dungeons and Dragons.
Which, yes, gets a bit bizarre.
If you're missing that 2d iso goodness from the golden age of RPGs, or if you just want to know what it would be like to use a rocket launcher to fight a demon, try out Shadowrun.
"Deus Ex: Human Revolution," "Deus Ex: Mankind Divided," and absolutely not "Deus Ex: The Fall"
The Deus Ex games feel to me like a friend you had in grade school that used to be a lovable nerd, that has now become cool at the expense of also being slightly insufferable. Like, I'm happy that they've become so successful, but I wish they didn't wear polo shirts and wreak of cologne.
The original Deus Ex game was an in-depth role playing experience wherein the protagonist was pretty much a blank slate for people to use to put themselves in the hero's shoes. This new generation of Deus Ex is objectively excellent with amazing gameplay and graphics. Unfortunately the cologne is Adam Jensen, the moody protagonist you're stuck playing. After an attack leaves him made out of half-a robot, Adam Jensen has his life saved with cybernetic enhancements that give him the super power to mope all day. Also super strength I guess.

Gravelly voice: "I''m super bummed about being able to crush bricks with my bare hands."
Teasing aside; these games are of superb quality. If you shut his dialogue off you can enjoy a masterfully envisioned cyberpunk version of Detroit, and in the sequel a cyberpunk version of Prague. The ability to sneak, hack, talk, or shoot your way out of pretty much any situation is incredibly gratifying.
In my play through of "Mankind Divided" I decided that my Adam Jensen was pretending to be a mopy cop as part of a long con, and now that he was in Prague it was time to steal everything. The heists I pulled off a conman Jensen were delightful, and I can't recommend this style enough. That said, one game there is no possible way to enjoy is "Deus Ex: The Fall."
If a fiscally irresponsible Bill Gates were to present you with one million crisp American dollar bills every time you smiled while playing "Deus Ex: The Fall" you would be no wealthier after an evening of playing this game. It is a horrific combination of terrible gameplay, nonsensical plot, joyless cash grab-bery. If you are tempted to play "Deus Ex: The Fall" do yourself a favor and slash your own tires instead. At least then you'll be able to explain where all of your money has gone in a more concise way.
"Until I have You"
It's true that I find RPGs to be one of the better styles of video game when it comes to exploring worlds, but they don't all have to be RPGs to be great. "Until I Have You" is a platformer, oddly, and it's use of action, perspective, and pixilated art is utterly addictive.
You start in media res as a cyber powered hero in a world that feels lost to greed. As the story of revenge progresses you are given hints that things are not what they seem, though you are powerless to do anything but move forward.

Although, to be fair, the main obstacle in your way is less solving a mystery and more this gentleman with the laser rifle.
As with most great cyberpunk, the world here is one of the characters. Seeing the details of this world was so much fun that I found myself watching every moment of cut scene happily, a rare feat for a game to accomplish.
Do not expect weeks of gameplay out of the main story here. This game is short, but it was a wise choice to end once it had showed off all it had to show. The story wrapped up nicely, and there's an amazing new game mode that unlocks at the end which lets you fight each boss consecutively. I highly recommend this game for anyone with even a passing interest in the cyberpunk genre.