For measuring power you need to measure AC Volts and AC Amps. Volts with a DMM, Amps with an AC Clamp. You need to blow a single test tone for the test as well, as voltage & amperage will change depending on frequency. 60hz is considered the standard point to test from.
When you have your results:
Multiply the VAC by the AAC for PMPO power.
Multiple PMPO by 0.707 for the approx. RMS Wattage. This is your true power.

Measuring using the method described in the quote doesnt work. Why ? Because impedence changes as the coil moves inside the motor (hook a DMM in ohmage range to a speakers terminals and push the cone for proof), it also changes with heat. Power applied to the coils causes them to heatup, changing the impedence.
So what I'm saying is, impedence isnt static ! That (quoted) measuring criteria requires the impedence to stay static.

Here's some figures to work with.. A JBL W15GTi duel 6ohm woofer, in 3ohm configuration, is connected to a JBL BPX2200 amplifier and measured with a DMM & clamp with a 60hz tone.

Static Impedence = 3ohm
VAC = 84V
AAC = 16A

Using the quoted method..
84 x 84 = 7056
7056 / 3 = 2352WRMS

Using the correct method..
84 x 16 = 1344 PMPO
1344 x 0.707 = 950WRMS

Why is the RMS power so low you ask ? Well thanks to ohm's law we know V / A = R (impedence load)..

84 / 16 = 5.25 ohm

So at 60hz this particular woofers actual impedence is 5.25ohm, almost 2x its Static Impedence. This is why the VAC^2 measurement method doesnt work.

if you use a fluke digital multimeter, note that most of them will read volts and amps in RMS already, so you don't need to multiply by the 0.707.

but I agree, you can't do it into a speaker with the ohm's method.
and using a test resistor won't be accurate either, as the amp's output will be different with an inductive load (speaker) compared to a resistive load (resistor).

This is true, a real speaker will present a complex reactive load on the amplifer, even depending on the enclosure.

To clarify things for others...

Measuring the actual amount of power* delivered to the speaker while playing a sine wave of fixed frequency is of limited value in the real world. (Basically only really useful to SPL competitors.)

This is because when you are playing music, the actual power delivered to the speaker will vary significantly.
Secondly, these are not long term measurements, they do not take into account how long the amplifier can output that power before overheating (and hopefully going into protection, rather than smoke - and the degree of protection circuitry can vary somewhat too...).

*Generally you'd measure the THD (total harmonic distortion) as well, 1% THD would be roughly at the point of clipping, above that point you can still get significantly more power out of the amplifier (yes, even at the fundamental frequency of the tone you are playing), but with much distortion.

Obviously this is only useful if the subwoofer can handle the extra power (without significant thermal compression), and it actually results in a higher SPL reading.

However using a resistor to measure the power output can still possibly be a useful way of comparing one amplifier to another. This is because almost all car audio amplifiers will respond in a similar manner to a reactive load.
That is why we talk about speakers having nominal impedance loads, so we can assume that one amplifier which was measured at producing 100w into a 4 ohm resistive load at 1% THD will be capable of similar output into a given 4 ohm nominal speaker when compared to another amplifer which was also measured with a similar output under the same conditions. (When the power output is measured for a significantly long period of time...)

The power measured in these examples is basically the average power over one sine wave, which is what people really mean when they state 'RMS power'. Power itself isn't measured in RMS, these values are simply calculated from the RMS voltage. Ie, if you measured the peak-peak voltage, you'd multiply that by 0.707 to get an approximate RMS voltage. Then the power is simply the voltage squared divided by the resistance as stated in the original post.
(This is only for a sine wave, determining the average voltage over a more complex wave requires much more complicated math..)

As Blackice mentioned, there are two significant factors which can increase the instantaneous impedance of your subwoofer, compared to the DC resistance. First, as you apply a significant amount of power to the coil, it will heat up, raising the DC resistance. Secondly (due to how a speaker works), the low frequency roll off of a subwoofer depends on the resonance of the speaker (including any effects of the enclosure, series resistance of the wiring etc).
Anyway, the impedance will reach a peak at the resonant frequency. So at that particular frequency, even though the impedance is larger (so the speaker is not recieving as much power), the SPL does not actually drop off much, since the speaker is operating more efficiently at that frequency.
(To clarify, I am not talking about ported/vented enclosures here, but the speaker itself)

There is also the inherent inductance of the voice coil, but this isn't as significant for subwoofers, since the inductance raises the impedance at high frequencies.

(some of these concepts would be a bit clearer with diagrams, but I'm a bit short on time right now)