Due to the high bandwidth requirements and stringent delay constraints of multi-user wireless video transmission applications, ensuring that all video senders have sufficient transmission opportunities to use before their delay deadlines expire is a longstanding research problem. We propose a novel solution that addresses this problem without assuming detailed packet-level knowledge, which is unavailable at resource allocation time. Instead, we translate the transmission delay deadlines of each sender's video packets into a monotonically-decreasing weight distribution within the considered time horizon. Higher weights are assigned to the slots that have higher probability for deadline-abiding delivery. Given the sets of weights of the senders' video streams, we propose the low-complexity Delay-Aware Resource Allocation (DARA) approach to compute the optimal slot allocation policy that maximizes the deadline-abiding delivery of all senders. A unique characteristic of the DARA approach is that it yields a non-stationary slot allocation policy that depends on the allocation of previous slots. We prove that the DARA approach is optimal for weight distributions that are exponentially decreasing in time. We further implement our framework for real-time video streaming in wireless personal area networks that are gaining significant traction within the new Internet-of-Things (IoT) paradigm. For multiple surveillance videos encoded with H.264/AVC and streamed via the 6tisch framework that simulates the IoT-oriented IEEE 802.15.4e TSCH medium access control, our solution is shown to be the only one that ensures all video bitstreams are delivered with acceptable quality in a deadline-abiding manner.