Close, but it is a ratio of the two impedances:
Damping factor DF = load impedance / source impedance
Load = speaker plus wires (remember there are two wires, plus and minus, to each speaker)
Source = amplifier output impedance
https://en.wikipedia.org/wiki/Damping_factor
If your 0.08 ohm Zout amplifier is driving an 8-ohm speaker that is a DF = 100. Most spec sheets only report a single number and only magnitude, so how much it varies over frequency (can be a lot) and how sensitive to a reactive load the amp may be are hidden. Note amplifier stability depends upon a lot more than just Zout, however.
I would not say it is a red herring, but is one factor (parameter) among many, and like any other spec should be consider with everything else -- including your speakers. In the 70's and 80's super high DF and super wide bandwidth were the rage for a while. There are drawbacks to anything taken to extreme, naturally, including lower stability and transient distortion from very high feedback to get high DF, and reduced stability and additional noise from super wideband designs. All is compromise...
One thing I tend to do is consider the impedance looking back from the speaker terminals, not the amplifier's output, to generate the effective DF seen by the speaker rather than right at the amplifier. This is not the commonly-accepted DF equation, but provides a better idea of what the speaker is going to do since that is the driving-point impedance it sees. That is,
DF' = Zspeaker / (Zamp + Zwire)
I remember reading, and this is a reference I really wish I had at hand, that damping factor over 20 is inaudible in most systems. Way back when, I decided anything over 100 in the LF region was not worth the trouble, but was looking at high-power amplifiers that usually have pretty low output impedance. SS amps I took a quick look at seem to range around 100'ish at 100 Hz or so, and tube amps can fall to the single digits. The latter is what makes them more sensitive to the speaker they are driving.
Note 10 feet of 14 AWG cable (20 feet total) is about 0.05 ohms, so if the amplifier was perfect (0-ohm output) that'd be a damping factor of about 8/0.05 = 160 measured at the speaker terminal looking back... If your amplifier has about the same output impedance (a DF of 160), then the effective DF' at the speaker is reduced to 80. probably in the mud as far as audible effects. Where DF matters is low-Z speakers and/or long speaker cables that are relatively small. Back then zip cord of maybe 24 to 20 AWG wire was not all that uncommon in a lot of inexpensive systems. Since then a lot of manufacturers have jumped in and raised awareness so most people are using 18 AWG and up for speakers, at least based on what I see and read around (anecdotal).
FWIWFM - Don