We introduce a one-dimensional plaquette orbital model with a topology of a ladder and alternating interactions between x and z pseudospin components both along the ladder legs and on the rungs. We show by an exact transformation that it is equivalent to an effective spin model in a magnetic field, with spin dimers that replace plaquettes and are coupled along the chain by three-spin interactions in the Hilbert space reduced by a factor of 2. Using perturbative treatment and mean-field approaches with dimer correlations we study the ground state spin configuration and its defects in the lowest excited states. By the exact diagonalization approach we establish that the quantum effects are of purely short-range nature in the model and we find estimated values of the ground state energy and the gap in the thermodynamic limit from the system sizes up to L=12 dimers. Finally, we study a class of excited states with classical-like defects accumulated in the central region of the chain to find that in this region the quantum entanglement measured by the mutual information of neighboring dimers is locally increased and coincides with disorder and frustration. Such islands of entanglement in an otherwise rather classical system may be of interest in the context of quantum computing devices.