How to reroute this downspout?
As "D-on" suggested, the best way to go is under the concrete path.  If you feel like replacing the cracked section, then pull it out, dig a trench, and extend the downspout through the trench (ductwork all the way). 
 Alternatively, dig a trench under the concrete and cut a hole directly below the downspout in the existing slab.  The drawback here is you will have trouble fully back-filling the trench after installing the ductwork.

Either way, you should then put in a drywell at the terminus.  Since the piping is below ground level, it can't empty into the garden in any case (unless you run the piping far enough that the ground has sloped down to its level, in which case crushed rock at the exit point will stop erosion)