Summary: This work studies a haptotactic cross-diffusion system modeling oncolytic virotherapy \[ \begin{cases} u_t = \Delta u - \nabla \cdot (u \nabla v) - \rho u z, \\ v_t = - (u + w) v - \kappa v, \\ w_t = D_w \Delta w - \xi_w \nabla \cdot (w \nabla v) - w + \rho u z, \\ z_t = D_z \Delta z - z - \rho u z + \beta w, \end{cases} \] in a smooth bounded domain \(\Omega \subset \mathbb{R}^2\), with parameters \(D_w > 0\), \(D_z > 0\), \(\xi_w \geq 0\), \(\rho \geq 0\), \(\kappa > 0\) and \(\beta \geq 0\). This system describes the interaction among uninfected and infected cancer cells, extracellular matrix and oncolytic viruses. It is rigorously proved that an associated no-flux initial-boundary value problem has a unique global classical solution which is bounded in \((L^\infty (\Omega))^4\). Moreover, it is shown that this bounded solution can approach a spatially constant equilibrium in the large time limit under the additional assumption that \(0 \leq \beta < 1\).