I don't think any pathfinding algorithm is best in all circumstances. In two tries I was able to draw a map that A* performed best on (714 operations, vs. 767 best-first, 803 trace). A* is pretty smart at trying likely routes. It seems if you draw a map where there is a long likely route that's actually blocked off at the end, and have a fairly indirect route to the target, then A* is sometimes fastest at working out the first path is a dead-end and then quickly identifying a route down the second path, whereas other algorithms sometimes revert to a slow iteration working backwards. Basically given arbitrary circumstances I think A* manages to never be terrible.
Wikipedia says A* "considers fewer nodes than any other admissible search algorithm with the same heuristic". The cost of running the search is also amortized by running it in a web worker, so it runs in parallel to the game and therefore shouldn't ever impact the framerate. So I think it's not a problem as it is.
Still, it's a very cool demo and great visualisation of how the algorithms work!