If you finely divide a magnet into tiny magnets and suspend these particles in a liquid, is that really a liquid magnet, or just a bunch of solid magnets floating in a liquid?
If you finely divide a magnet into tiny magnets and suspend the particles in a liquid, you get... a normal ferrofluid. It's magnetic in the presence of an external field, but will lose its magnetization once that field is removed. This is because permanent magnetism (i.e. ferromagnetism) is a bulk property.
Every atom has a magnetic moment, but they are normally randomly aligned and thus the macroscopic field cancels out. It's only when these moments are aligned that a macroscopic magnetic field arises. Permanent magnets have the requisite crystalline structure for this to happen. As you chop it up, this macroscopic organization is destroyed.
If you get into the details, what they've done is to use the surface tension of the oil-in-water to "jam" an outer layer of magnetic particles and prevent them from rotating, thus preserving their magnetic alignment. This, in turn, is apparently enough to keep the free-floating, unjammed particles inside the droplet aligned as well, thus turning the entire droplet into a magnet. Pretty interesting, because without the membrane, none of the ferrofluid is magnetic, but with the membrane, all of it is.
More of a jam, since it contains solids. ;-)
In this case, it's a liquid magnet down to roughly the scales of the nanoparticles, which is only a bit bigger than the atomic scale on which nothing is a normal liquid.
https://physics.stackexchange.com/q/242654/7911
There are better example from condensed matter physics.
They clearly cannot do so because macro sample would lose its properties. It simply cannot be tiny magnets suspended in a liquid. You gotta provide finer definition of a liquid because it typically does not have a structure. In your example there are constraints to movement and position of tiny magnets.
On one side your right, this isn't really a "liquid magnet", but on the other, this behaves like a magnet while retaining many of the properties of a liquid.