As @sezare56 points out, all what we hear is “real analogue” sound. So we are talking about sound generation and perception of sound.
Technically speaking …
I guess, there will be no dispute about analogue sound, if the complete sound creation is made of analogue circuits only. But if the sound is created completely or partialy with digital devices there is the question, is this a “digital sound” then?
I would say, it depends and I will try to explain …
Human Perception of Sound …
Our perception of sound has developed by evolution and has a quite long time been under the influcence of sounds generated by the natural environment only. Those sounds have been created all mechanically - maybe with the exception of the thunder, which has some electro-mechanical origin.
Most mechanically created sounds of nature have the characteristic that they are never stable or constantly keeping a tone. There is much fluctuation to natural sounds, which is sometimes quite subtle, but it’s there in any case, and that has been ingrained as “natural” in our brains for tens of thousands of years. Everything, which does not fit in this archtype of sounds, has a pretty good chance to be perceived as “un-natural”.
AFAIK, the very first electronic instruments have been based on analogue electronic parts and circuits, which had broad margins with respect to their physical properties and which where quite sensitive to fluctuations of the environmental temperature additionally. This - no wonder - created sounds with a lot of unstability and fluctuations, and which seems to fit quite well to our perception of “natural-like” sounds.
The first digital instruments had very low digital quality, compared to standard parts of today. Low sampling rates caused aliasing, low bit-rates didn’t get all the detailed information of “natural-sound”. The results have been sound artifacts, which our perception was not used to hear. Additionally the algorithmic processes of early digital instruments generated a flow of numbers, which translated to a much more accurate sound, than any natural sound could be.
Those two issues have been early addressed and became also attributes of “digital sound”, which had been called, as an example:
- “cold”, which IMO is the lack of fluctuation and addition of strange frequencies, or
- “too HIFI”, which IMO is too clean and too accurate, or
- “metallic”, which is the result of aliasing and had not been treatet good enough with anti-aliasing. Aliasing creates artificial frequency “side bands”, which are often perceived as “wrong” or “metallic”.
IMO “digital sound” could be described as:
- having a considerable amount of aliasing, other digital artifacts, or too much lack of natural fluctuations, or
- which is technically only possible with digital and/or algorithmic processes
We have many digital instruments today, which are capable to generate sounds, which most listeners could not tell apart from a real analogue source, even in an A-B comparison 
Now back to the initial question … what could be “analogue sound”?
IMO “analogue sound” is equivalent to a sound, which is perceived as “natural sound”. And this would be independent from the true sorce of the sound.
I hope this post was not "too extensive " 