Temporal modeling remains a fundamental challenge in video understanding, particularly as sequence lengths scale. Traditional video models relying on dense spatiotemporal attention suffer from quadratic computational costs for long videos. To circumvent these costs, recent approaches adapt image models for videos via Parameter-Efficient Fine-Tuning (PEFT) methods such as adapters. However, deeply inserting these modules incurs prohibitive activation memory overhead during back-propagation. While recent efficient State Space Models (SSMs) introduce linear complexity, they disrupt 2D spatial relationships and rely on extensive masked pre-training to recover spatial awareness. To overcome these limitations, we propose Parallel Kinematic Selective State Space Scanners (PKS$^4$). We retain a standard 2D vision backbone for spatial semantics and insert a single plug-and-play PKS$^4$ module with linear-complexity temporal scanning, avoiding temporal attention and multi-layer adapters. We first extract kinematic priors via a Kinematic Prior Encoder, which captures local displacements and motion boundaries through inter-frame correlations and differences. These priors drive linear-complexity SSMs to track underlying kinematic states, adaptively modulating update speeds and read-write strategies at each time step. Instead of global scanning, we deploy parallel scanners along the temporal dimension for each spatial location, preserving spatial structures while reducing overhead. Experiments on spatial-heavy and temporal-heavy action recognition benchmarks show that PKS$^4$ achieves state-of-the-art performance. Remarkably, our method converges in merely $20$ epochs, achieving approximately $10\times$ lower training compute than pure video SSMs, establishing a new paradigm for efficient video understanding.