One of the most influential games ever actually embraced processor lag—and it became an extremely popular game mechanic!
While programming the iconic game Space Invaders, the game's creator Tomohiro Nishikado discovered that the fewer aliens on the screen, the faster the processer was able to render them. This meant that as the player destroyed more of them, the remaining aliens would move faster. Another way to look at this is the processer being burdened and lagging towards the beginning of the game and being freed up as you get further.
Instead of changing things around to keep the speed consistent, Nishikado decided to just leave it the way it was as a challenging gameplay mechanic. In other words Nishikado, quite by accident, created a game which increased in difficulty as you progressed, an idea that almost all modern games utilize.
Today, Space Invaders is viewed as one of the most influential games of all time. Up until the release of the classic shooter in 1978, video games were just virtual representations of something else. Space Invaders was also the first shooter in which the enemies fired back. On top of that, the game popularized the idea of high scores as well, as it was the first to save a player's score.
Possibly even more importantly, multiple well-known game developers have stated that the game is what got them interested in video games in the first place. Among these developers is Shigeru Miyamoto, the creator of classics such as Super Mario Bros., Donkey Kong, The Legend of Zelda and Star Fox.
Those are just some of the many influences Space Invaders has had on the world of video games. Indeed, it has quite the resume. Who knows where video games would be without it.