You are right, essentially this is Dijkstra. However, I would appreciate you to be a bit more specific in your answer. As Dijkstra is broadly used and known algorithm, while LiveWire is its exact application that we use here for image task. In order to avoid any misunderstanding, I would prefer "LiveWire" or "Dijkstra in application to delineation problem".
Also, this is not a full point as question requires to provide a clarification "What properties of the road edge make it applicable?", why this method is the best here. So, "LiveWire" by itself would not help to reach a full point without full answer.
Dijkstra algorithm is one of the most basic algorithms in computer science. It aims at optimal finding the shortest path in the graph, it can be seen from a dynamic programming perspective if you wish.
Image delineation tool, so-called LiveWire, is one of many fancy applications that use Dijkstra algorithm in its core.