I'm no expert but I have built a few amps myself now, including a few tube amps, a First Watt, and two Ncore amps so I have a better understanding of the power rating situation than I did previously.
As stated, Hypex actually gives more information than others, and if you know how to read it, it gives a much better picture of the capabilities of the amp. Why should they quantize their information to fit only the RMS slot just because that's what consumers mostly kind of understand? Their modules are also geared towards integrators so the information is helpful, not misleading.
Let's take an example, the First Watt amplifiers. These are rated in the most straightforward way, and it's easy to understand. The rails on these amps run at 24V. Therefore, there is no way to ever exceed a little bit less than 24V output signal to your speakers. Taking into account losses due to source resistors and R(on) of the transistors let's say it can swing 20V (hard ceiling, absolutely no more).
Into 8 ohms, given V^2/R you have 20^2/8 = 50w peak. Peak does not mean peak as in short bursts like others have said. It's a mathematical reference. Now to get RMS you can work out the actually formula, but it actually turns out to be peak/2 so you have 25W RMS.
Now imagine an amp that is similar to the First Watt above but the rails are 50V and not capped at 24V. But it can"t swing up to 50V all the time continuously because of thermal reasons, but it still can swing into the 40V range for seconds at a time delivering your bass notes and loud passages and peaks and such undistorted even. This amp perceptibly would be a much more capable and powerful amplifier even though it couldn't sustain a 40V / 1kHz test signal on the bench for an hour while you go and make a bacon lettuce and tomato sandwich. So it fails the RMS continuous lab test, but it still can get louder than a rail limited amplifier like the First Watt or other similar topology.
Considering the quasi-sinusoidal nature of music, this gives you a hell of a lot more power than the continuous RMS criteria can show. Some amplifier topologies can take advantage of this, while fixed rail limited amps cannot. That's why RMS continuous ratings are not quite everything and we need a few other parameters to tell the story.