Wow, how atrocious! I don't mean what the internet is doing to our brains (I'm not too worried about that), but the mangling of science.
The correlation-is-not-causation problem is egregious here. Maybe depression causes people to use the internet more. Or some third factor (low self-esteem; bad impulse control) causes both depression and excessive internet use. Maybe people with lower amounts of white matter in the regions listed have less ability to control their impulses or regulate their time on the internet - that's actually plausible.
The only way to get around the correlation problem is to randomly assign some people to use the internet (people who have never been on it before, mind you) and some to stay the hell off it, and then measure changes in depression, white matter, etc. over time. It might be that studies have actually done this, but this blogger sure doesn't explain it that way.
One modicum of truth here: multitasking does make people perform very badly at all the tasks their doing. However, I'd take "stress, reduced thinking speed and creative ability" with a grain of salt. Could be true, but I don't think we have a good body of evidence for those things.
And... having skills for finding information, instead of storing it all in your brain... Isn't that what every librarian tried to teach us in school? Isn't that a good thing? I dunno. I think the internet only makes you dumber if you use it in a dumb way.