I don't know about others, but there's really no chance I'd be physically able to read those words without things like this. My eyes blur and I feel a physical strain on them - like I'm trying to do some type of eyeball aerobics.
I literally can't read more than about a sentence without having to look away a few moments and then return.
I can read grey on grey just fine, even on my old laptop with its terrible color and worse grey resolution. Moreover, that site isn't grey on grey, it's grey on light cream ( https://en.wikipedia.org/wiki/Cream_(colour) ).
If you haven't already, go to a doctor and get your eyes checked out. What you're describing is not typical.
http://i.imgur.com/X78sHxx.png
Note that the links behind the blue translucent rectangle are unclickable.