  We construct the non-stationary Ruijsenaars functions (affine analogue of the
Macdonald functions) in the special case $\kappa=t^{-1/N}$, using the
intertwining operators of the Ding-Iohara-Miki algebra (DIM algebra) associated
with $N$-fold Fock tensor spaces. By the $S$-duality of the intertwiners,
another expression is obtained for the non-stationary Ruijsenaars functions
with $\kappa=t^{-1/N}$, which can be regarded as a natural elliptic lift of the
asymptotic Macdonald functions to the multivariate elliptic hypergeometric
series. We also investigate some properties of the vertex operator of the DIM
algebra appearing in the present algebraic framework; an integral operator
which commutes with the elliptic Ruijsenaars operator, and the degeneration of
the vertex operators to the Virasoro primary fields in the conformal limit $q
\rightarrow 1$.
