https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#Dynamic...
Although the shortest path problem has some kind of "optimal substructure", the recursive memoized approach doesn't work because there's no set order in which the subproblems can be solved. Instead, you need to compute the shortest paths in order of shortest path length, and the shortest path lengths aren't given ahead of time - those are exactly what Dijkstra's algorithm computes!
It's not enough to call it dynamic programming that "the shortest path must be the shortest path through one of its neighbors", because this fact doesn't immediately lead to an acyclic subproblem dependency graph.
Shortest path on an acyclic graph, and longest path on an acyclic graph, are two problems that can be solved with dynamic programming - but Dijkstra's algorithms solves shortest paths on a different class of graphs that doesn't lend itself to DP.