The ambiguity lies in how exactly this is interpreted, and in particular whether passive moves (here, f.ex., being dragged along by another piece) count.
There is precedent in the very Problemist issue this variant was introduced in: Petkov's discussion of ‘Half‐neutral’ pieces includes an exaample where a HN R in white phase (see the article for further details) can castle with the white K, implicitly without changing to its neutral phase (as would happen if the R moved on its own) and thereby giving check; thus at least in that context Castling is explicitly treated as an K move which only incidentally causes the R to change position too.
Standard Chess leaves this kind of situation entirely unspecified as relevant situations can never arise: the only (potentially) passive move is castling, and once that's happened the K has moved and so further castling is prohibited.
The ambiguity lies in how exactly this is interpreted, and in particular whether passive moves (here, f.ex., being dragged along by another piece) count.
There is precedent in the very Problemist issue this variant was introduced in: Petkov's discussion of ‘Half‐neutral’ pieces includes an exaample where a HN
Rin white phase (see the article for further details) can castle with the whiteK, implicitly without changing to its neutral phase (as would happen if theRmoved on its own) and thereby giving check; thus at least in that context Castling is explicitly treated as anKmove which only incidentally causes theRto change position too.Standard Chess leaves this kind of situation entirely unspecified as relevant situations can never arise: the only (potentially) passive move is castling, and once that's happened the
Khas moved and so further castling is prohibited.