It's hard to tell if this site is advocating for ditching this type of js library altogether and writing all those replacements inline (ick for some of those) or simply replacing jQuery with a thinner (and narrower) library.
I could be convinced of the latter but not the former.
One of the main things we're advocating is to consider not depending on jQuery when building an open-source project.
For Offline, PACE, Odometer, Tether, and many of our other OS projects (http://github.hubspot.com), we chose not to depend on jQuery because it means our libraries can be smaller and more people can use them.
We're happy and proud to use jQuery when building an application. As many other commenters have noticed, it can be extremely useful at reducing code complexity—and let's just say it: it can make it more enjoyable to write front-end code!
I think that what it's saying is that you can write yourself a microlibrary that just includes the ten or fifteen lines of adapter code you actually need for the thing you're building, and that you should use native browser constructs whenever possible.
I could be convinced of the latter but not the former.