  We explore the semi-classical relation between the fuzzy 4-hyperboloid
$H_N^4$ and non-compact quantized twistor space $\mathbb{P}^{1,2}$ at large
$N$. This provides two backgrounds $N$ of the IKKT matrix model via two natural
stereographic projections, leading to higher-spin gauge theories with Euclidean
and Minkowski signature denoted by HS-IKKT. The resulting higher-spin gauge
theory can be understood as an uplift of $\mathcal{N} = 4$ super Yang-Mills to
twistor space. The action of HS-IKKT is written using a spinor formalism in
both Euclidean and Minkowski signature. We then compute the tree-level
amplitudes of the massless sector within the Yang-Mills part of the HS-IKKT
model in the flat limit in Euclidean signature. All $n$-point tree-level
scattering amplitudes for $n \geq 4$ of this sector are found to vanish in the
flat limit.
