This post is predicated by this video:
In it, Razbuten points out some really interesting things about his wife playing video games like Shovel Knight, The Last of Us, and Doom (2016). He noticed how there are things that gamers take for granted (waypoints, buttons that aren't always labeled, game mechanics not lining up with real world mechanics) that his wife simply couldn't comprehend. I found it fascinating that this came up, and it had me think about what games I would choose to expose someone to gaming.
1: Super Mario Bros.
Rabuten chose this game, and I'm in agreement. World 1-1 is still a gold standard for teaching the basic mechanics of a game without overtly telling the player what to do. It is simple, encourages exploration, and allows the player to get a feel for the world in a way that isn't excessively challenging. It's a great way to start out, especially given it's age.
2: Dance Dance Revolution

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I might be a wee bit biased, but I think this game is a great way to show the positive benefits of gaming to someone who has no idea. The one problem with DDR is that it's...not exactly the most intuitive. That said, with a little bit of coaching, some explanation, I think this game would be a ton of fun for someone who doesn't play video games. It would probably spark an interest in gaming when it finally clicks.
3: Mario Kart 8 Deluxe

Sure, sure, this could be replaced with any one of the Mario Kart games, it's an excuse to drop my Amazon Affiliate link, but the point still stands. Mario Kart is a great game to get people into gaming. It's easy enough to learn how to play, but still challenging enough to make you work for your wins. And it's also great for showing people how to lose friends! And yeah, that is an affiliate link. You buy the game, you help me out. Full disclosure, and all that.
4: Doom (2016)
I gotta say, I agree with Razbuten. This is a great game for sharing with people who are new to gaming. There is a certain level of badassery that comes with being DoomGuy. There's something sadistically satisfying about stunning an imp, coming up behind it, and ripping its head off right at the jaw. It also does a decent job exposing players to new concepts as the game progresses. Razbuten talked about the gore hive, and how the game taught his wife to get up close and personal with the shotgun. When learning game mechanics feels intuitive and rewards you for doing it right, players will want to learn more about it.
Personally, I think gaming is a great thing to share with everyone. It's play in its purest form, a child-like joy with a little bit of rivalry along the way. Why wouldn't I share that with others?