Fourier transform technology
Well, Fourier theory is behind every kind of equalizer. We wouldn't know what "equal" means without; the Fourier transform is how we know how to describe a signal in the frequency domain, and that's what ends up being "of equal power everywhere" after an equalizer.
If we interpret "technology used in the guts" as "does it employ a Fourier transform during operation":
That fully depends on the type of equalizer! The whole class of Frequency-Domain Equalizers are based on it. But even if you have something like a 12-band EQ made of biquad sections, somehow, somewhere you need to find the "is" state of the observed spectrum to make an equalizer actually equalize and not just arbitrarily shape the spectrum. And the Fourier transform is the standard way of doing that.
Any suggestions for references to gain an understanding on how digital equalizers are implemented?
I'd say: start with about any good DSP textbook; mine was a German one co-authored by one of my favourite lecturers, so that got me hooked on DSP. then, I read Oppenheim/Schafer's Discrete-Time Signal Processing, which I bought for a handful of Euros used; having had but a short glimpse into Richard G. Lyon's (he's on here, nice person) Understanding Digital Signal Processing seems quite nice, as well. I think that's the book I'd recommend to you, or maybe his more introductory The Essential Guide to Digital Signal Processing, which I think is more for management-level, less for people who are/have been already studying electrical engineering, math or similar topics.
Sooner than you'd like you'll appreciate the Fourier transform, its discrete-time variant (DFT, as usually implemented by an FFT), and what you can do. It will also tell you where all the formulas that just happened to appear in the website you link to come from!
Now, I'm from a communications engineering background, so the kind of equalizers we build have a different application than those that people in the audio signal processing trade build. Their mathematical construction, however, is the same, as the job of an equalizer is always to remove the effect of echos that constructively and destructively overlay with the original signal, or, identically, since the impulse response (i.e., when do the echoes come, and at which phase and amplitude) and the frequency response (i.e., how does the room==channel==system attenuate and phase-shift different frequencies) are inherently the same information – linked through the Fourier transform!