It looks like the author was referring to this: “In relativity theory, a horizon is also a boundary on the region which an observer can see. Horizons pose an issue for warp drives as one cannot control the warp bubble if one see or communicate with it.”
And for more context, the author seems to note that faster than light travel is possible under Einstein’s physics: https://www.sciencealert.com/faster-than-light-travel-is-pos...
https://hal.archives-ouvertes.fr/hal-00981257/document#:~:te....
Also, even if the claim about the Casimir Effect is correct, since the Casimir Effect occurs between a pair of uncharged plates, the "warp bubble" would have to be between the plates--but that means the warp bubble can't move the plates, so using it as a "warp drive" would not be possible.
That said I think you still need such huge energies that it's impractical.
The geometries in question don't generate negative energy, they are generated by negative energy (which actually isn't a very good term for the kind of stress-energy that is involved). This paper is just talking about different possible geometries that could exist between Casimir plates, based on different possible configurations of "vacuum energy" that could exist between the plates. Even if one of these geometries turned out to be a "warp bubble", it still wouldn't change the issue that I described before, that all of this is taking place between uncharged plates, and the plates are outside the "warp bubble" so the bubble can't move them, so this is not a viable option for an actual "warp drive".
He's talking about a highly speculative form of "warp drive" he has proposed that supposedly does not require negative energy, as all previous "warp drive" solutions (such as the Alcubierre drive) did. His speculations have not been accepted as valid by other physicists working in the field. (Also, calling such travel "faster than light" is problematic, since a light beam emitted from inside a "warp bubble" would still outrun the bubble itself. These are really just highly counterintuitive spacetime geometries that are most likely not physically possible anyway because the kinds of materials that would be needed to create them don't exist and can't be manufactured.)
Reworded: "Horizons pose an issue for warp drives as one cannot control the warp bubble if one can't see or communicate with it."
The problem, then, is that warp drives as posited create KVF horizons that would seem to make them impossible to control, enter, or leave. That would mean warp drive is not permitted in the universe.
Some KVF horizons, like the outer ergosphere of a black hole can be detected, entered, and exited. Conclusion, warp drives are not ruled out on the grounds that they involve horizons because we don't know what kind of horizon they might have.
tl;dr Warp drives aren't ruled out... yet.
Granted this article is largely above my reading/comprehensive level, but after describing multiple types of horizons and then saying a wrap drive horizon largely resembles a black hole horizon, I can't see where the author actually defines "the horizon problem".