  We consider the Gaussian approximation for functionals of a Poisson process
that are expressible as sums of region-stabilizing (determined by the points of
the process within some specified regions) score functions and provide a bound
on the rate of convergence in the Wasserstein and the Kolmogorov distances.
While such results have previously been shown in Lachi\`eze-Rey, Schulte and
Yukich (2019), we extend the applicability by relaxing some conditions assumed
there and provide further insight into the results. This is achieved by working
with stabilization regions that may differ from balls of random radii commonly
used in the literature concerning stabilizing functionals. We also allow for
non-diffuse intensity measures and unbounded scores, which are useful in some
applications. As our main application, we consider the Gaussian approximation
of number of minimal points in a homogeneous Poisson process in $[0,1]^d$ with
$d \ge 2$, and provide a presumably optimal rate of convergence.
