These are recordings of a sample of parts from instruments.
Those are traditionally regarded as being analog, although in recent times I've seen people claiming they're not, since they use discrete instead of continuous signals. So they're kind of halfway.
The Mellotron is an analog multi-sample sample-playing instrument. It's just that working in analog makes everything way more cumbersome.
Your usage of sample is correct, but there are other usages of the word which are alos correct, and the term "sampler" isn't specific to the literal digital signal sampling.
I have bought and made plenty of sample packs, to be played back by various sample players, over the last 25 years. A "sampler" refers to how the device works with recordings, not the individual digital samples that it makes up- as far as I understand it anything that allows you to recontextualuze short recordings is a sampler,
A mellotron very much is a mechanical sampler, though very limited compared to its current digital counterparts.
I am open to being wrong. But your claim is a bit odd. While I'd be stoked to see some evidence in the philology of the term that says I'm wrong, I just don't think that is something you'd find.
Is there a strong reference? I know that's in wikipedia, and the primary reference appears to be https://www.soundonsound.com/techniques/lost-art-sampling-pa.... As much as I love SOS, this is rather flimsy evidence that Fairlight "coined" the term.
I think we agree that it's irrefutable that the use of the term sample in the past 30 years is unrelated to digital vs. analog both on wikipedia and numerous scholarly and printed works. That doesn't speak to origin of the term of course. The OED doesn't cite uses prior to 1985, FWIW.
The Mellotron is still alive and well, both as a mechanical instrument still supported and made by Streetly Electronics, and in digital form by the official plug-in versions from GForce Software like https://www.gforcesoftware.com/products/m-tron-pro/ . I suppose with the plug-in virtual Mellotron the sounds really are samples.