  We implement type-II seesaw dominance for neutrino mass and baryogenesis
through heavy scalar triplet leptogenesis in a class of minimal
non-supersymmetric SO(10) models where matter parity as stabilising discrete
symmetry as well as WIMP dark matter (DM) candidates are intrinsic predictions
of the GUT symmetry. We also find modifications of relevant CP-asymmetry
formulas in such minimal models. Baryon asymmetry of the universe as solutions
of Boltzmann equations is further shown to be realized for both normal and
inverted mass orderings in concordance with cosmological bound and best fit
values of the neutrino oscillation data including $\theta_{23}$ in the second
octant and large values of leptonic Dirac CP-phases. Type-II seesaw dominance
is at first successfully implemented in two cases of spontaneous SO(10)
breakings through SU(5) route where the presence of only one non-standard Higgs
scalar of intermediate mass $\sim 10^9-10^{10}$ GeV achieves unification. Lower
values of the SU(5) unification scales $\sim 10^{15}$ GeV are predicted to
bring proton lifetimes to the accessible ranges of Super-Kamiokande and
Hyper-Kamiokande experiments. Our prediction of WIMP DM relic density in each
model is due to a $\sim$ TeV mass matter-parity odd real scalar singlet
($\subset {16}_H \subset$ SO(10)) verifiable by LUX and XENON1T experiments.
This DM is also noted to resolve the vacuum stability issue of the standard
scalar potential. When applied to the unification framework of M. Frigerio and
T. Hambye, in addition to the minimal fermionic triplet DM solution of $2.7$
TeV mass, this procedure of type-II seesaw dominance and triplet leptogenesis
is also found to make an alternative prediction of triplet fermion plus real
scalar singlet DM at the TeV scale.
