I think your question goes more toward impedance matching of the speaker to the amp, rather than "what is a watt?"
I am no expert, but I will copy the explanation that Coincident Speaker Technologies gives:
Loudspeaker Impedance And Amplifier Matching
Solid State Amplifiers:
With transistor amplifiers ,the amp's output impedance is never matched to the load it drives.The lower the load impedance ,the closer it comes to a true impedance match , because the output impedance of a solid state amp is very low - typically a fraction of an ohm.This helps explain why (all things being equal- and the amplifier has sufficient current capability)4 ohm speakers produce greater acoustical output than 8 ohm speakers.The lower impedance speaker offers less resistance to current from the amp.The transistor amp sees less resistance into 4 ohms , therefore its output stage delivers more current.
A tube amplifier's output stage(s) are totally different. A true match between the load impedance and the plate impedance ( or plate - plate impedance of a push - pull tube output stage) is never absolutely possible.The tube's plate impedance is typically exceptionally high
( thousands of ohms.) Therefore ,even a tube output transformer ( which becomes necessary to lower the plate impedance so that a typical speaker can be driven) with a primary impedance of 3K - 8K ohms will not closely approach this match. Therefore, it can be seen that the operation of tube versus solid state outputs is reversed. In the case of transistors, impedances cannot be matched due to the ultra low output impedance of the amp ,while with tubes, the match cannot be achieved because of the very high output impedances.
The output transformer in a tube amp lowers its impedance to a level where speakers can be made to operate and extract power from the driving amplifier. The output transformer is designed with a given ratio between the number of turns of wire in the primary and a nominal secondary impedance. For example, if we connect an 8 ohm loudspeaker to an amplifier with a primary impedance of say, 5,000 ohms and a transformer tap of 8 ohms, the primary impedance remains at 5,000 ohms and the amplifier delivers a given amount of electrical power. But ,if a 4 ohm speaker is connected to this amplifier, the output volume will diminish because the 4 ohm load causes a reduction of the primary winding impedance. This reduction means the amp's output transformer presents a poorer match to the plates of the tube output stage than it previously did.
On the other hand, if a 14 ohm loudspeaker is connected to the same 8 ohm tap, the primary winding's impedance is increased. The transformer represents only a ratio of turns and its impedance is determined by the load connected to it. Because the transformer's impedance has increased, it comes closer to matching that of the plate circuit. The result is greater output volume from the speaker.
In conclusion, a tube amplifier will produce more output ( greater voltage delivery) into higher impedance loads. Therefore , a 14 ohm speaker will be much more efficiently driven by a tube amplifier than will a 8 or 4 ohm speaker. This becomes of critical importance when using OTL or single ended triode tube amplifiers when available output power is low and amplifier output impedance is very high.
To fully realize the inherent potential of al SE triode tube and OTL amps , a loudspeaker of 14 ohms or greater is mandatory. Anything less involves a huge compromise.
Now that you are likely totally confused, as I was when I first read this, I think the main point is that, based on impedance matching, if you are using a high impedance speaker, then a tube amp will produce greater volume with less power, and conversely, a solid state amp will require greater power to get the same volume from the same speaker. At least that's how I understand it.
If I am totally off base, I hope some electronics whizz will set us straight.