> More constructively, I wonder if recent Linux distros and desktop environments actually run better on 10-year-old hardware than Windows 7.
This depends entirely on the desktop environment / window manager.
The machine described in the article uses Xfce. As a real-world example of its low requirements, I very recently setup an old Dell laptop running openSUSE 13.2 with Xfce; said laptop has a single-core processor and somewhere between 512 and 1024 megabytes of RAM (I forget the exact number). Runs like a champ, while a "modern" version of Windows would - in my experience - choke even with much more resources at its disposal. I've also run Xfce-based setups on even weaker hardware, though at that point you start to run more heavily into performance issues.
You can go even lighter than this, of course, by switching to a plain window manager instead of a full-fledged desktop environment. Tiny Core Linux, for example, uses FLWM (a lightweight FLTK-based window manager); combined with its use of busybox instead of the GNU userland, it's able to run on as little as an i486 and 42MB RAM. That's a bit on the extreme end, though, but going a bit bigger than that, I've had good experiences with Openbox (and similarly lightweight window managers) on a full GNU/Linux system running on systems with Pentium II processors and less than 256MB RAM.
Heavier desktop environments like GNOME, Unity, and KDE certainly have additional performance impacts, especially due to their heavy reliance on compositor effects. However, in most circumstances, a system with 1-2GB RAM and a mid-200x single or dual core processor will handle these fine. In the case of KDE, you can also turn off desktop effects, thus reducing computational overhead even further.
In the Windows world, you can generally get a system comfortably to the same realm by turning of Aero (in the case of Windows 7). I'm not sure what the customization options are for Windows 8/8.1/10, but I expect the option for a "Windows Classic" look/feel still exists, and I further suspect that it would allow some additional usability. However, in my experience, Windows is quite prone to slowing down over time; even with routine maintenance (defragging non-solid-state drives, running CCleaner, etc.), performance will typically degrade over several months to a year after installation. For newer hardware, this isn't a huge problem, but for older hardware, this becomes a significant obstacle to usability that GNU/Linux and BSD systems don't typically have.