If you're using the "Manhattan metric" (each step north,
south, east, or west counts as one unit of distance) as
seems likely in this case, the slope isn't going to be
useful for reducing the distance. OTOH, if the grid is
mostly unobstructed, Dijkstra's will try to search outward
in a diamond pattern, which could be a lot slower than
something that simply tries to connect the dots. That could
be important in, for example, a video game AI. Depends on
what your exact requirements are.
BTW, that prohosting website is really and truly ugly.
Turn on my cookies and try again? Not likely.