  The Koornwinder-Macdonald multivariable generalization of the Askey-Wilson
polynomials is studied for parameters satisfying a truncation condition such
that the orthogonality measure becomes discrete with support on a finite grid.
For this parameter regime the polynomials may be seen as a multivariable
counterpart of the (one-variable) $q$-Racah polynomials. We present the
discrete orthogonality measure, expressions for the normalization constants
converting the polynomials into an orthonormal system (in terms of the
normalization constant for the unit polynomial), and we discuss the limit $q\to
1$ leading to multivariable Racah type polynomials. Of special interest is the
situation that $q$ lies on the unit circle; in that case it is found that there
exists a natural parameter domain for which the discrete orthogonality measure
(which is complex in general) becomes real-valued and positive. We investigate
the properties of a finite-dimensional discrete integral transform for
functions over the grid, whose kernel is determined by the multivariable
$q$-Racah polynomials with parameters in this positivity domain.
