I've worked on my game for about a month in the public, only to realize that it has no purpose. There's no actual meat to the burger, if that makes sense, it's just all the other toppings you would put on a burger, and while good, isn't really what you want from a burger. So, I come to ask, how do you give purpose to a game? Unlike a burger, games are very complex and require a lot more meat than just beef. I'm open to anything that could help me.

To give purpose to a burger, you must be hungry.
For a game, you must be bored.

What i mean is: You do not give purpose to a game yourself. The players do.

If that doesn't help, maybe talk more about the game and it's issues, than about burgers. ; )

I think you don't mean purpose. You mean spice and fun.

You could offer people playtesting your game and ask about what they think what would be good.

Games satisfy a lot of elements. The need for play, feelings of growth, feelings of learning, feelings of accomplishment, feelings of empowerment, multiplayer games can give social rewards, stress relief, and some games teach real-life lessons. They can (and should) do many of them at once.

It's also context dependent, as others mentioned. One person find a game compelling, another person doesn't. Also, one day a game is popular and trending, the next it's yesterday's news and nobody cares for it.

As for how to do it, you've just discovered a massive field of study. If you find a definitive answer then game designers, psychologists, and business executives everywhere would love to know it. Otherwise, it is something people iterate on, talk about, and try to understand in ways that are unique to every game.

A purpose can be as simple as trying to get the highest score, kill the big bad boss, or acquire the golden macguffin. Maybe some kind of back story is progressively revealed as you progress. These may be simple ideas and we may have done these things many times before but they can be a enough to hook us into playing for awhile.

Another random though is that, if you don't already have some, music can really set the tone for your game and hook the player a bit more.

abyssal said:
I've worked on my game for about a month in the public, only to realize that it has no purpose. There's no actual meat to the burger, if that makes sense

Maybe it needs an overarching goal, with a desirable and satisfying story outcome for the player to strive for.

Or maybe it needs to have some real-world social benefit. Encouraging players to become activists for the climate or homelessness, for example.

abyssal said:
I come to ask, how do you give purpose to a game

People usually skip on the basics of economy, then they are surprised they run their projects to bankruptcy. First do a precise market research, speak hundreds of people in the community you are eying with, research the possible demands and calculate what you should do.

If you develop the game without this, and expecting people to turn up, that is not going to work, unless you wrote the game strictly for your own entertainment, when profitability is not in focus.

Why don’t you try adding what interests you personally? There’s no one-size-fits-all formula

As Frob mentioned (beautiful post, btw), the entertainment or value of a game can come from many different places. Make it interesting, or make it rewarding, or make it so it teaches people something, or make it all of the above. Dopamine and curiosity are powerful things!