If you wanted a simple way to implement it (performance on this sort of game would not be affected), you could simply get the tile clicked on and then:
1) work out if it's on the same horizontal or vertical line as the space,
2) calculate how many spaces away from the space, and
3) loop moving one space in the correct direction.
I'm glad you added it, though. It makes a big difference to the playability with the mouse!