Yeah. Houka should be King, Nonon should be Bishop, and Satsuki should be Queen.
That would imply that Honnouji Gakuen would fall if Inumuta dies or is even cornered, which definitely is not the case. This image works just fine if you keep each chess piece's meaning to its supposed roles and importance, not strength.
Because Jakuzure being the strongest among the Daevas doesn't make much sense either. Gamagoori would actually be the closest to a Queen due to his loyalty, but there's still the association that Queen must be female so yeah.