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So when I was a kid, I remember reading a book about a kid playing a popular videogame, except all over the world, ships are starting to appear less and less in the levels. At one point, he's restarting the game and the very first three easy ships appear, and send him a message with a picture of some weird eggs with legs and something like "Please don't shoot! There are children on board!"

He looks into it more, and instead of just being a glitch he finds out that there's actually a world inside the game, and each time people reload the videogame they're actually fighting new, different ships of an alien species and they're running out and almost dead.

The kid transports into the other world somehow, and meets with the alien queen (they're bugs of course, I think the author was a fan of ender's game or trying to cash in on it or something), and helps them just stop showing up to battles so that there are no more ships in any of the games any more and they don't have to die. He returns to earth (I don't remember how) and everyone is returning the games because there are no more enemies and levels can't be completed.

I recall the name being like, "Disc World" or something, but that can't be right since discworld is an actual thing and very popular. Can anybody help?

This sounds like "Only You Can Save Mankind" by Terry Pratchett.

"...send him a message with a picture of some weird eggs with legs and something like 'Please don't shoot! There are children on board!'"

The alien spaceship is in his sights. His finger is on the Fire button. Johnny Maxwell is about to set the new high score on the computer game Only You Can Save Mankind.

Suddenly, a message appears:
We wish to talk. We surrender.

"all over the world, ships are starting to appear less and less"

the ScreeWee have disappeared altogether from everyone else's copy of the game

Terry Pratchett is also the author of the Discworld novels, which may be the cause of your confusion.