  We study the one-loop effective action of the higher-spin gauge theory
induced by the IKKT matrix model on a $\mathcal{M}^{1,3}\times \mathcal{K}$
background, where $\mathcal{M}^{1,3}$ is an FLRW cosmological spacetime brane
and $\mathcal{K}$ are compact fuzzy extra dimensions. In particular, we show
that all non-abelian ($\mathfrak{hs}$-valued) gauge fields in this model
acquire mass via quantum effects, thus avoiding no-go theorems. This leads to a
massive non-abelian quantum $\mathfrak{hs}$-Yang-Mills theory, whose detailed
structure depends on $\mathcal{K}$. The stabilization of $\mathcal{K}$ at one
loop is understood as a result of the coupling between $\mathcal{K}$ and the
$U(1)$-flux bundle on space-time. This flux stabilization induces the KK scale
into the $\mathcal{N} = 4$ SYM sector of the model, which break superconformal
symmetry.
