That’s the question in the OP: are there ways, theoretical though they may be (since there’s no need, what with digital recording and all that), to record sound in an analogue format besides what we have now (viz, grooves in a wax cylinder or vinyl disk, or a magnetic tape)?
*I ask because I’m kicking around a short story in my head about a non-Earth civilization and wondering how they could record sound.
Wire recorders Wire recording - Wikipedia are magnetic, but don’t involve tape.
Film uses variations in opacity to record sound.
Basically, any method that can store varying quantities of something could be used.
You could use a wire that varied in thickness, for example.
Like this:
The area on the right edge with two “squiggly” areas is the analogue stereo soundtrack of that particular format of 35mm projection film.
This technique encodes analogue sounds by variations in the brightness of light passing through the soundtrack area and decoded by optoelectronic sensors.
I was going to post the analog soundtrack on film. But since that was taken, how about this:
Grooves placed in the tarmac that are “decoded” by shaking the vehicle going over it.
The first method of recording sound in general is the phonautograph. Vibrations recorded on smoked glass. There were some half-hearted early attempts to convert them so they could be played back (using groove based methods) but they weren’t successfully played back until 2008!
The oldest known audio recording comes from one of these. Au Clair de la Lune.
Holography. There is nothing inherently digital about holography and analog holographs are just about the highest resolution method of capturing analog information.
I think that gets disqualified for the same reason a player piano roll or a music box do. It’s not so much a recording as it is a replication.
At the risk of muddying the waters a bit around phonograph records, the original groove system recorded oscillations left and right versus the baseline spiral that encoded silence. When stereo was introduced, a couple of different systems were tried. But the one that won out encoded the sum of elft+ right as lateral oscillations about the baseline spiral for backwards compatibility. And encoded the difference L-R as variations in groove width which caused the stylus to oscillate vertically as it entered narrower or wider areas of groove.
So right there are two very different recording techniques just involving grooves. You could design an “anti-record” that instead had a raised ridge that a read head shaped something like a tiny car could ride along the crest of. YOu could design one where another “dimension” of sound was record by some torsional twisting of the surface and hence the reading device.
Unrelated to the above you could use wire of varying thickness, width, cross section, or even electrical or magnetic conductivity.
No, a player piano or music box triggers a musical instrument to play a specific note. A car is not a musical instrument and the grooves in the tarmac are not triggering specific notes. The grooves are single impulses, whose spacings are converted to audio frequencies. It’s actually quite similar to a record player’s vibrating needle.
As a bit of a historical note, when stereo vinyl records began to be mass-produced starting in the late 50s and through the 60s, there was a transition period when records were produced in both mono and stereo versions. This was the period when stereo record covers were distinguished from their mono counterparts by often garish logos announcing that they were Stereophonic, Living Stereo, Dynamic Stereo, Panoramic Stereo, Full Stereo, Stereorama, Stere-O-Phonic, and other such marketing claptrap.
The coexistence of the two formats was because although stereo pressings were in theory backward compatible with mono cartridges (at least in the sense that you could play them and get sound) in most cases the mono cartridges of the day would excessively wear and damage the stereo records if indeed they could play them at all without skipping. The reason was that the stereo channel information was recorded at 45º angles on the two walls of the groove, which caused the stylus as you say to oscillate vertically as well as laterally, and most mono cartridges of the time didn’t have the vertical compliance to track those complicated grooves properly.
Back in those days, in fact, your typical portable record player wouldn’t even have a magnetic cartridge, but rather one with a ceramic element, which required (by modern standards) a fearsome amount of tracking force, which mono cartridge would likely destroy a stereo record on the first play. I believe the size and geometry of the stereo stylus was also different. Eventually stereo records and the cartridges to play them were pretty much universal and mono records disappeared.
I thought it got disqualified because “Besides Grooves Pressed Into A Medium.”
I don’t think using concrete cutters count as “pressed”. 
Alec (Technology Connections) has also done a video about how LPs reproduce stereo.
I haven’t watched it myself yet, but I wanted to post the link before someone else ninja’ed me.
This is not quite what the OP is asking for, but it’s an interesting related idea.
There’s an old idea that it might be possible to play back sounds that were inadvertently recorded during the making of pottery or applying paint. The idea was that sound would subtly modify the position of the tool being used, whether a potter’s stylus or a paint brush, so that ambient sound was recorded. It doesn’t look like any significant sounds have been reproduced from such possible recordings. Wikipedia puts the topic under “Discredited thories” of the Archaeoacoustics page:
How about punched tape like that used in teletype machines?
While this is a groove based method, RCA had a product called a Capacitance Electronic Disc, which rather than the variances in the groove being read physically, it was read electronically. The stylus stays fixed in the groove, and the capacitance between stylus and disc is what changed as the groove’s walls go in and out. They got much higher information density this way, totally analog as well.
Seems digital not analog
I note the subject includes “Even Theoretically”.
The were several types of analog delay line memories back in the day. While things like mercury tubes were for early computers and digital, still earlier ones were analog. In digital terms maybe one or two thousand bits. But delay times of only microseconds. Plus there’s the degradation from reading, amplifying and writing the info over and over.
But … theoretically with modern tech those numbers could be ramped up somewhat. Maybe someone could “record” a 2-3 minute song with an extended version of one of those methods.