In this technical note, we study the relations between the local stabilizability of a class of input-affine discrete-time nonlinear systems and their local Quadratic-Supply-Rate (QSR)-dissipativity properties. Focusing on stabilizability by linear Static Output Feedback (SOF), we derive several sufficient conditions for Lyapunov stabilizability based on QSR-dissipativity. A closed-form expression for the SOF stabilizing gain is derived from the QSR matrices. Additionally, we prove that necessity also holds in some special cases. The QSR-dissipativity-based conditions provide an alternative to the traditional Passivity-Based Control (PBC) by allowing for a more general input-output behavior, i.e., non-passive dynamics. Numerical examples illustrate their applicability for designing stabilizing controllers for open-loop unstable systems.