The weakness of the queen isn't peculiar to Byzantine -- that's standard Medieval chess. The modern hyper-powerful Queen came about only at the *very* tail end of SCA period.

Broadly speaking, period chess is like modern, except:

-- Queens move one space orthogonally;
-- Bishops have a short leap of two;
-- Some of the weird fiddly bits (castling, the initial pawn move) were occasional variants, rather than standard.

Overall, the result is a slower, more strategic game, with less of a tendency to turn suddenly...