There is a large difference between chess sets intended as tools for playing chess games, and sets intended for display by collectors. The latter are actually not chess sets at all; they are works of art inspired by chess.
While I agree that some Chess sets are more suitable for playing the game than others are, this wasn't the pertinent issue. The Chess variant pieces flanking the logo are not Chess pieces, and they will not be used to actually play Chess. Instead, they serve the decorative purpose of conveying the idea of Chess variants, and this purpose has its own criteria.
First, they should bear enough of a resemblance to what people commonly think of when they think of Chess pieces. For this purpose, resembling Staunton pieces works best, though the reason is for the strong association between Staunton pieces and Chess and not for the superiority of Staunton over some other design. Despite being anthropomorphic, the current Fairy Princess bears enough resemblance to the Staunton Queen for someone to spot the similarity. In the same way, the Tenniel illustrations of the Red Queen on the 404 page also resemble a Staunton Queen. Despite being more fully figurine, the Dragon Horse resembles the Staunton Knight enough to look like some kind of Chess variant piece.
Second, they should differ from the Staunton pieces in some significant way. The Dragon Horse has enough dragon features to tell it's not an ordinary horse, and the Fairy Princess has butterfly wings. These features help evoke the idea of being different from the usual Chess pieces we are normally familiar with.
While I agree that some Chess sets are more suitable for playing the game than others are, this wasn't the pertinent issue. The Chess variant pieces flanking the logo are not Chess pieces, and they will not be used to actually play Chess. Instead, they serve the decorative purpose of conveying the idea of Chess variants, and this purpose has its own criteria.
First, they should bear enough of a resemblance to what people commonly think of when they think of Chess pieces. For this purpose, resembling Staunton pieces works best, though the reason is for the strong association between Staunton pieces and Chess and not for the superiority of Staunton over some other design. Despite being anthropomorphic, the current Fairy Princess bears enough resemblance to the Staunton Queen for someone to spot the similarity. In the same way, the Tenniel illustrations of the Red Queen on the 404 page also resemble a Staunton Queen. Despite being more fully figurine, the Dragon Horse resembles the Staunton Knight enough to look like some kind of Chess variant piece.
Second, they should differ from the Staunton pieces in some significant way. The Dragon Horse has enough dragon features to tell it's not an ordinary horse, and the Fairy Princess has butterfly wings. These features help evoke the idea of being different from the usual Chess pieces we are normally familiar with.