Some problems do not give you an explicit graph, but the state space forms a DAG. For example, in a grid where you can only move right or down, each cell is a node, and edges represent valid moves. The grid is a DAG because you cannot return to a previous cell (moving right and down is acyclic).
You can apply DP by processing cells in row-major or column-major order. Many classic DP problems are secretly DP on implicit DAGs: knapsack, edit distance, and grid path problems.