Dijkstra is not limited to summing edge weights. It works for any metric where the triangle inequality holds: dist[A][C] <= dist[A][B] + dist[B][C]. For minimax paths, the triangle inequality becomes: max_effort[A][C] <= max(max_effort[A][B], max_effort[B][C]).
This holds, so Dijkstra works. The algorithm structure stays the same. You redefine how you combine costs: instead of addition, you use max(). This pattern appears in network routing, image segmentation, and other domains.