This paper presents a receiver-driven video delivery algorithm that exploits a novel Randomized Network Coding (RNC) scheme for unequal error protection (UEP). The main idea of our approach is to account for the unequal importance of media packets in the network coding algorithm for efficient stream delivery in lossy overlay networks. Based on the requests from their neighbours, the network nodes properly combine packets and forward them to their children nodes. The network coding operations at every node are formulated as a log-concave optimization problem, which is solved with a greedy algorithm in only a few iterations. Our experimental results demonstrate that the proposed scheme permits to respect the priorities between the different packet classes. It further outperforms baseline network coding techniques for video streaming in overlay networks.