Issues with Modern Games, or, How to Engage a Game's Community

This is an important topic because I think that we're starting to stray away from everlasting games. Before I go on, great games are still made, and I do get excited when I hear about all the cool games my friends are playing and all the features they have, sometimes it's just amazing what is being developed.

We're going to step back to learn from some of the original big-time game creators, and see when we can learn.

NOTE: TL;DR AT END

Multiplayer

This goes without saying, and is definitely still implemented a lot. It's also become much easier to implement with all the helpful tools that exist for networking. From what I know, Helldivers 2 and Fortnite are actually really good examples of this. People want to play with real people, especially their friends.
Now, long distance multiplayer is a bit hard, especially for indie or solo developers, but there are alternatives.
Firstly, you can implement local multiplayer. This is much simpler, and would allow multiple players to spin up their own "server" to connect to and play together.
Secondly, there's same machine multiplayer. This was a favorite of flash games back in the day, where you would squeeze onto one keyboard with your friend to battle each other. This shouldn't be your first reach these days, and it would be much nicer to have local multiplayer instead.
If you want to implement multiplayer into your game, I would suggest looking into websockets, or alternatively, your game engine may have network capabilities all there ready for you.
Multiplayer is an easy way to get a community going for your game, people love playing against each other, or even together to beat a goal. You may be developing a single player game though, and there are cases where a game is objectively single player, but don't stress, there are other things you can implement to boost your community.

Speedrunning

Speedrunning is one of the most interesting parts of a game's community. Most modern games have many speedrunners, which is good, but what makes a game more "speedrunnable."
Back in 1993, DOOM was released. After completing a level, you were met with an intermission, which gave you some statistics about your run. Importantly, there was the time it took you to complete the level, along with a par time. Imagine how great it would've felt to beat your friends time by a single second. It's no wonder that DOOM's speedrunning community is still strong over 30 years later. So if you can, maybe consider adding a timer to your game.
That's not the only thing DOOM did well, there was also a recording method that created what was called "demos". These recorded the player input and saved it to a file. This was important (especially back then) because a demo file was considerably smaller than a video file, making it easier to transport. Moderators also got to take a look at each frame of input to see what a person was doing, which is great for cheating checks. This feature isn't too hard to implement, especially on smaller games with fewer possible inputs.
Games these days usually use regular recording and third party timers for speedrunning, which is fine and works just fine. Just think to yourself while you're developing your game whether people would even want to speedrun your game.

Competitive Play

Quake's deathmatch, Fortnite's battle royale, Rocket League's... battle?
It's like multiplayer, except against real people, on a large scale. The biggest games are the ones that end up as esports. The grind that players go through to optimize strategies, whether it's map control, or hitting a ball into the goal every time.
Once you've implemented multiplayer, try to make a competition or tournament around your game. Make people want to be the best at it, and spend a lot of time learning all the intricate mechanics you implemented (whether on purpose or accidentally).
If you aren't able to implement multiplayer, it may be useful just to add a simple leaderboard system, where player's aren't battling in real time, but there's still a world-wide competitive aspect.

Modding

In my opinion, this is the most important factor that will boost a game's community.
People still make DOOM maps to this day, and will probably continue to do so. There are a few reasons that modding keeps a game alive so well.
Firstly, you can only make so many features, levels, and so on, so why not let the community make infinitely more than you ever could? If modding isn't implemented, what you make is it, that's the end of the game. Image if DOOM was 3 episodes and that was it. However, with the aspect of modding, you can download and play maps, allowing you to play the game for much longer. You may think this would take away from sales of your game, however, DOOM II sales were massive
Secondly, modding of features, not just maps. Sure modding a new level is cool, but being able to add new guns, new characters, new textures, ultimately will create an entirely new experience in your game, to the point that it's unrecognizable. This also can lead to new games being developed from your game, such as Quake being the base for many, many games.
Even though I think this is the most important part of a community, it seems to be done less. Or at least it's harder to do. Imagine if you could create your own level for triple A games, the community would go crazy. Ultimately, I think what may kill this is game engines. Game developers don't create a level editor, so they can't give it to the community.
Personally, I'm creating an animation tool for my game studio, and it works with an external script to control the animation of the characters. All a modder has to do is learn the very simple language of that script, and they will be able to add whatever animation they want. This wasn't even the original plan for my tool, but I would be stupid to turn down the community by redacting the animations.

TL;DR

I do think this is a long block of text, so here's a simpler version.
There are 4 aspect that will boost a game's community.

1. Multiplayer (WAN, LAN, same machine)
2. Speedrunning (Timer, recorder)
3. Competition (FFA, Team Battle, etc.)
4. Modding (New levels, new features, animations)

Out of all of those, I personally think modding is the most important.
Try as hard as you can to cater to these communities, and your game will be the better for it