Autoregressive diffusion transformers (AR-DiTs) recast video generation from an offline paradigm to a real-time streaming one: the model generates video one chunk at a time, making each chunk available for playout once produced. The service-level objective (SLO) for this paradigm is no longer fixed latency or throughput but the preservation of playout continuity: generation must stay ahead of the playout timeline. Once generation falls behind, the remaining playable buffer (playout slack) is exhausted, and users experience visible stalls. This objective reveals two serving design insights. First, real-time video generation has a dynamic SLO that evolves with playout progress, so resources should move toward streams with lower playout slack. Second, an acceptable chunk delivered on time is preferable to a late high-fidelity chunk, so per-chunk fidelity configurations should adapt to available playout slack. Guided by these insights, we present SlackServe, a playout-slack-driven serving system that preserves playout continuity in real-time streaming video generation. SlackServe uses playout slack as a unified signal, reallocating resources across streams through three-tier priority queues, re-homing, and elastic sequence parallelism, while selecting per-chunk fidelity configurations within each stream through Bi-Modal Pareto Routing under a quality floor. On a 16-H100 GPU cluster, SlackServe improves Quality of Experience (QoE), measured by Continuous Play Ratio (CPR), by 1.64x-3.29x and reduces Time to First Chunk (TTFC) by 1.61x-9.65x over baselines, while preserving comparable generation quality.