I was playing in Minecraft with a friend making a redstone system with minecarts, at one point I approached the darkness and saw some semi-transparent circles that took up the entire screen. I think it's a lighting bug or something but I'm not sure. I wait for answers...
I don't see a semi-transparent circle in that image (it actually looks almost entirely Black and just about all I see is your hand and some... strange thing on the right side, but that doesn't take up the entire screen so I doubt that is what you're referring to)... but I'm wondering if what you're seeing is the vignette on the edges of the screen and for some reason noticing it only when the color is uniform? Although with the entire scene being entirely Black that doesn't sound likely, but it's the only circle taking up the full screen I can think of.
They probably have their display set incredibly bright (as so many seem to nowadays, i blame the trend towards "dark themes", which I don't understand at all either, especially since most just look like complete blackness with dark gray/colored text and are hard to read, as if they are trying to compensate for the brightness of a display which makes the text look white (at the same time, on LCD displays this ruins their ability to show darkness, and wastes energy/display life since the backlight is always on at the full screen brightness, and the greater changes in brightness from "dark" to "light" content can be uncomfortable). It may also be that they are in a completely dark room (I was always taught to have proper lighting, no using computing devices in bed when you are supposed to be sleeping).
I used Gimp to set the brightness and contrast to near their maximums and it does show a series of circles, although it doesn't show that well in this case due to the lack of variation in color levels:
This would indeed be caused by the vignette, but simply because it is so dark there are only a few possible graysxale color values that can be used to represent the gradient (the RGB values on the original image shows a range of 0-2 for the area which shows the circular pattern, thus only 3 values are being represented. Given that there is actual pure black they must be using some mod since vanilla definitely does not have complete darkness, nor does your display affect the pixel values in a screenshot (I believe the only thing that does is "clear type", which adds red/blue fuzzing around text to make it look better, and can vary from display to display/system to system and does show up in screenshots so it isn't just an on-screen change).
Aside from a better combination of display and in-game settings to increase the color range for near-dark values (you are still relatively limited here; the Wiki claims that full darkness on Moody is 5% of full brightness, decreasing towards the edges due to the vignette, and gives about 13 grayscale levels on a linear scale, which can still be noticeable) you could disable the vignette (I believe I've seen that Optifine, if not vanilla, has a setting for this in newer versions, otherwise, you can use a resource pack to replace the original texture). I never cared for it myself due to the reduction in visibility in caves and I always played on Fast until I modded the game to remove it on Fancy (Optifine also makes it possible to individually set everything to Fancy so this is about the only difference). Note that there may be some other parts of the game that use the texture, e.g. the end credits, and just replacing the texture will affect that, but you hardly see it anyway.