I don’t think this change in the minimum requirements was attached to a certain version of Blender, as in “Blender 2.xx will not run anymore, if those requirements are not met”. I guess it was more like: “Whoa! We just realized that we still have minimum requirements from the late 90s on our website. Could someone please change this already?”
Anyway, minimum requirements are about “user expected performance” as well as sheer capability. So, read this more as: “this is what we think is a very basic system to have a halfway fluent user experience. Blender might very well run on older machines, but don’t expect to have much fun with it and don’t complain if some features are broken”.
And let’s be frank: Those old requirements were very old indeed and long overdue for an overhaul, as Blender had progressed quite a bit over time and technology lept forward as well. Not sure how many machines with the old specs or lower were even still around in 2013, let alone used for 3D work. And even the new requirements should be met by almost any machine built in the last - let’s say 8? - years…
Why don’t you experiment with different versions of Blender for yourself and see which one gives the best performance to available features ratio? After all, Blender has to run to your liking on your hardware.