First, let’s make sure no-one’s talking at crossed purposes: a sampler plays back sounds that already existed. A sequencer automatically plays an instrument, controlled by its electronics instead of directly by a musician. That instrument may or may not be a sampler.
I think the guide these people are writing (and please correct me if I’m wrong), saying “they are not played to make sound”, is talking about a sequencer, but conflating it with a sampler, perhaps? Which would be very understandable, as the popular Akai MPC range, and the Fairlight CMI, are both in a single device. Microcontrollers happen to be good at both these things, so they tend to get lumped together.
So if it’s direct human control of each note as it’s sounded that’s the criterion of what is and isn’t an instrument, then it’s sequencers, not samplers, that should be excluded.
(If making original sounds is the criterion, then samplers would be excluded.)
Having said that, we’re getting deep into the philosophy now of what is and isn’t an instrument. Maybe “instrument” is the right word, maybe not, but quantised, automatically played, sequenced music has a very distinctive sound, and I for one would appreciate the opportunity of browsing my music collection based on which releases have that sound. You’ve got the eight-looped-equidistant-notes sequencing of the Moog that’s integral to the whole Berlin school genre; the sixteen-looped-equidistant-notes-with-portamento-and-accents of the TB-303 that’s integral to the whole acid house genre. You’ve got the Art of Noise, Frankie Goes to Hollywood, and the rest of the ZTT label building a distinctive sound out of the CMI. The MPC series is well represented in hiphop. The 808 with its sixteen-looped-equidistant-notes is integral to techno and electro. The sequencer may or may not count as an instrument, but it’s something that’s helped to spawn whole genres. I’m not sure it can be dismissed. But it might be considered a distinct piece of studio gear, separate to instruments… Except sometimes it’s a small part of those instruments. So perhaps an attribute. Or not.
I certainly wouldn’t consider the MPC-60, TB-303, or Moog System 55 to not be instruments, just because they have a sequencer in them.
As with all of this, it can get messy and nuanced when you try to assert anything definitively.