Start with Tetris when he's 4-5 years old. It's an incredibly simple game with very simple controls. It has almost no text, no story, no suggestive imagery... Perfect for a little kid. It's literally an electronic puzle. With it he will learn the basics of gaming controllers and the art of pushing a button/performing an action on screen. And of course Tetris is great for the mind.

If he likes it and once he gets the hang of Tetris, try a simple 2D Platformer. Something like the original Super Mario Bros.: you walk/run right and left, you jump, you throw fire sometimes... and that's about it. Don't pick something with lots of power ups or with lots of mechanics like grabbing stuff or double jumping... The idea is that after learning to use a controller and to apply some logic with Tetris, he can try to navigate through a 2D World.

After that he will be able to try some slightly more complex games. When he learns how to read (more or less), you could give him something more text-heavy and intrincate like Pokémon. I think that franchise is perfect for introducing children to their first "adventure". Of course, he will get lost, he will struggle to learn some mechanics... but he will eventually get it. And of course you'll be there to guide him.

If he gets this far... then I would let him decide what he wants to play next (with limits, of course. Don't give him CoD for the love of God xD). You can make suggestions of course, but choosing by himself will develop his tastes. He doesn't have to like the same as his dad. Who knows, maybe he'll want to check a 3D game next. Whathever it is, keep playing with him. Maybe not all the time, but be there for him and have fun with him.

Whathever games you choose to use and whenever you end up introducing him to videogames, I encourage you to always play with him. Don't let him alone while playing, specially until he's like 9-10 years old. First because you have to make sure he doesn't play too much and because he'll need guidance both to understand how everything works and to not be alone if something weird appears on screen. And second because you gotta make him understand that videogames are something that can be enjoyed in company.

I tried getting my daughter to play games when she was around 2-4.  The only game she could really play well with us was New Super Mario Bros Wii.  (Even Mario Kart was really too hard at this age.)  With Mario she could run and jump with us and whenever the game got too hard she would go into a bubble.  You'll probably have to wait until your son is about 4 to even get 11th place or better on 50cc Mario Kart, but I guess they could play with guardrails on.

Start out with NES/Genesis/SNES stuff. Or 32 Bit platformers like Mario 64 and Spyro. I started at 4 to 5 years old and was able to completely master a lot of platformers by age 8. Lots of modern games just aren't designed for kids at all. Either that or they have the baggage of having 20+ years of complexity added onto them.

My 2.5 year old had great fun with Wii Sports Resort, watching the plane crash over an over, the guy jumping out. That got him into games. Motion controls are very intuitive early on, walking around with the analog stick is more difficult. 2D games or games with a trailing camera are preferred. Driving is very hard and easily frustrating. The best games are those you can play together, Knack is perfect for that.

iPad was also a hit, simple touch screen games. Then they started playing Roblox with their nephew around age 6. Now at 10 and 12 they're into Fortnite, Minecraft, Ark with school friends online. The youngest plays a lot on Switch. Online gaming is great with the pandemic. They can play with their friends right when online learning is done and when the weather is nice they coordinate meeting up at the park through party chat.

Anyway, early on, anything colorful with simple shapes that you can play co-op is perfect. Preferably something where one player doesn't run out of lives and gets locked out or restart. Hence Knack was so good.

My coworker has a 6 years old boy who just beat Horizon Zero Down (in the easiest difficult mode of course). I talked with him and he was surprisingly well versed in the game mechanics, knew what were the best bows, how to stealth, how to collect items to craft potions, etc

Curious is he doesn't know how to read yet except by a few words, he played solely guiding himself by icons

But overall sandbox games seems nice for kids. They can go almost everywhere and the lack of a real hurdle can get them entertained for months. Guess that's why kids love Minecraft

Don't over think it, let them just go to it organically rather than try and force anything.
Games can be for all ages.

Personally I wouldn't let anyone touch my gaming collection or Cheetos covered hands on my controller, but I would be more than happy to purchase them a console with a couple of their favorite games.

I wouldn't worry about it, let it happen organically when he becomes interested in your hobbies and wants to participate.


Also... "I have a 27 month old son"

It's time to stop using months.

He's 2.

All I would advise is for him to not get into games too early. I think 7-8 is a pretty okay starting age. That's when I started with GameCube and Game Boy Advance. I did dabble in a few PC edutainment titles when I was 5-6.

As far as screen time goes, I think television and film are preferable for younger kids, when they do have screen time that is. I think it's too early for games, smartphones, and most use of a computer.

Avoid gaming, introduce him to books, then enjoy watching him achieve and make something of his life 

I've started with my first kid when he was around 3....with flash games (it was a thing back then) for kids no less, which had only one input (usually space on keyboard), then he started playing more complex (input wise) games, until I let him try Wii and onward.