I don’t think sample really implies it has to be digital at all. “Sampling” can mean what you said, but I think a mellotron is very much a sampler by most definitions. It plays back a chunk of a pre-existing recording.
More than that, it plays back a particular snippet of audio recording, over and over, upon pressing a particular key. Play a different key and you get a different recording, and they're not meant to be heard once, they're meant to map to the sounding of a particular note, whether that be played staccato (playing only from the attack) or legato (playing the full length of the sample).
The Mellotron is an analog multi-sample sample-playing instrument. It's just that working in analog makes everything way more cumbersome.
