  One-dimensional gapped phases that avoid any symmetry breaking have drawn
enduring attention. In this paper, we study such phases in a bond-alternating
spin-1 $K$-$\Gamma$ chain built of a Kitaev ($K$) interaction and an
off-diagonal $\Gamma$ term. In the case of isotropic bond strength, a Haldane
phase, which resembles the ground state of a spin-$1$ Heisenberg chain, is
identified in a wide region. A gapped Kitaev phase situated at dominant
ferromagnetic and antiferromagnetic Kitaev limits is also found. The Kitaev
phase has extremely short-range spin correlations and is characterized by
finite $\mathbb{Z}_2$-valued quantities on bonds. Its lowest entanglement
spectrum is unique, in contrast to the Haldane phase whose entanglement
spectrum is doubly degenerate. In addition, the Kitaev phase shows a
double-peak structure in the specific heat at two different temperatures. In
the pure Kitaev limit, the two peaks are representative of the development of
short-range spin correlation at $T_h \simeq 0.5680$ and the freezing of
$\mathbb{Z}_2$ quantities at $T_l \simeq 0.0562$, respectively. By considering
bond anisotropy, regions of Haldane phase and Kitaev phase are enlarged,
accompanied by the emergence of dimerized phases and three distinct
magnetically ordered states.
