  The one-dimensional gapped phases that avoid any symmetry breaking have drawn
enduring attention. In this work, 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 double-peak
structure in the specific heat at two different temperatures. In the pure
Kitaev limit, the two peaks are representative of developing of short-range
spin correlation at $T_h \simeq 0.5680$ and 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.
