My suspicion is that the info in the book relies on single-crystal x-ray diffraction experiment (1), where geometry of selenium oxydichloride cannot be determined solely from MO principles. So, here is the structure of dioxane-seleninyl-dichloride:

As far as you can see, Se1
atom has three more neighbors: O1
from another $\ce{[SeOCl2]}$ unit, and O2
+ O3
from dioxanes. The bond angles correspond to those you discovered in the book, $\angle \ce{Cl1-Se-Cl2} = 95.6(3)$, and $\angle \ce{Cl1-Se-O} = 101.6(7)$:
The reason for that is given in the paper as well:
APPLICATION of the Gillespie-Nyholm theory to the molecules of
seleninyl dichloride, $\ce{SeOCl2}$, ... leads to the same prediction
for each: pyramidal geometry with the fourth position of a
tetrahedron occupied by a lone pair. However, more detailed study of
many non-metal compounds containing lone pairs has shown that the
Gillespie-Nyholm approach gives an incomplete description of the
bonding. The central atoms very frequently form additional bonds, of
greater length than the primary covalent links. In the case of
pyramidal molecules, it has been found that there are often three of
these secondary bonds, completing a distorted octahedron around the
central atom. Striking conformation of this has come from complexes
(or solvates) of $\ce{SeOCl2}$. All show $\ce{Se-O}$ and $\ce{Se-Cl}$
secondary bonds, with distorted octahedral geometry, although in some
cases the third secondary bond opposite the $\ce{Se-O}$ bond may be
significantly longer than the other two secondary bonds. Furthermore,
there are rare examples where a secondary bond has been replaced by
two longer contacts, and it may be inferred from these results that
the steric importance of the lone pair of electrons on $\ce{SeOCl2}$,
varies. In those cases where an octahedron can be observed, the angles
$\ce{X-Se-Y}$ ($\ce{X, Y}$ = $\ce{O}$ or $\ce{Cl}$) have been found to
lie in the range 142 -- 173, and there appears to be no clear way of
deciding which atoms, chlorine or oxygen, are going to form the
secondary bonds. The present structure of $\ce{SeOCl2 * C4H8O}$, is,
however, the first in which $\ce{SeOCl2}$, is involved in three
secondary bonds to oxygen with the $\ce{SeOCl2}$, being classed as
amphoteric.
Original
Long story short, your assumption would probably be correct for the "idealized" molecule in gas phase, whereas in reality there always will be a distortion as $\ce{As}$ strives to complete unsaturated coordination environment.
(1) Alcock, N. W.; Sawyer, J. F. J. Chem. Soc., Dalton Trans. 1980, No. 1, 115–120. DOI 10.1039/DT9800000115