“High levels of contrast” in the research literature always means as high as possible, but depends on the study’s capabilities. Old studies found that the highest level of contrast is best, but they were unable to achieve levels of contrast that modern monitors can. Modern studies that are able to reach these high contrast levels still show that readability is best at the highest possible contrast. So, in the context of current monitors, there is no benefit to withholding available contrast.
One thing to consider is that different monitors show colors differently. I checked three monitors; the grey text varies in how black it is, ranging from a mild nuisance to requiring 50% higher font size. The off-white background ranges from unnoticeable to a very minor annoyance, but does not seem to impact readability significantly. I don’t think an off-white background is a good thing, but the penalties are kept small by how close to white it is.
I guess if this will be a typography post, I’ll summarize what I know of the research on colors:
Dyslexia: I’ve seen claims that pure white text on pure black font causes problems. There is at least one paper on this subject, but I don’t think I necessarily believe this guideline without further studies, or at least without some testimony from an unbiased sample of dyslexic users.
Astigmatism: Pure white text on pure black background is very bad; lower the contrast ratio. Other color schemes are ok.
Poor vision: Make the contrast ratio as high as possible. W3C sets 4.5:1 as a minimum, but that’s not something to aspire to.
Black text on white (standard): Almost every paper claims this to be the best. Within this mode, they have found that contrast should be as high as possible.
White text on black (inverted): Increase line spacing compared to standard colors. Some users are more familiar with inverted colors. For normal users, contrast should be as high as possible, but this can cause problems in specific circumstances. Note that contrast is higher with inverted colors than with standard colors; I’ve seen claims that inverted colors can be better for people with poor vision.
Strange colors on strange colors: Raise the contrast as high as possible, or use hues that contrast with each other as a secondary tool. Some colors have poor performance (red), not just for colorblind users.
User preference: Familiarity with a color scheme does not just impact user preference, but also helps readability. Subjective preference is strongly correlated with objective readability on a population level. EDIT: This is a population-level correlation, so it’s not clear if individual expressions of subjective readability override population-level objective measures. That is, your evaluation of a color scheme will probably match the research. But if your evaluation differs from the research, it is not yet established whether your individual performance under that scheme will mirror the research or your expressed preferences.
One thing I’ll emphasize is that on recent Windows systems, outside of specific disabilities, changing text to gray has inferior outcomes because ClearType has the ability to adjust stroke width. It’s basically a blurrier font.
Edit: The link you’ve cited (ianstormtaylor) only mentions avoiding pure black as a background. That’s true, because white on pure black causes severe issues for some users, as well as creating transition problems when users switch between white and black screens. But it has no relevance to pure black text on white backgrounds. ianstormtaylor finds that some major applications prefer grey-black over pure black, and such applications are likely to have design powerhouses behind them. Continuing this trend of reasoning, I’ll note that grey-black backgrounds are semi-popular, pure black backgrounds are semi-unpopular, black-text-on-white is universal, and grey-text-on-white is extremely rare (except in Atom).