The damage dealt to the target is dealt by the original source of damage, not by Outrider en-Kor.

After Outrider en-Kor's activated ability has resolved, if multiple sources would deal damage to Outrider en-Kor simultaneously that turn (which can happen if Outrider en-Kor is blocked by multiple creatures, for example), you choose which source has its 1 damage redirected. If Outrider en-Kor's ability has resolved more than once that turn, you may choose a different source for each redirection effect.

If the targeted creature leaves the battlefield after the activated ability resolves but before Outrider en-Kor would be dealt damage, the damage isn't redirected away from Outrider en-Kor. The same is true if the target is no longer a creature (or a planeswalker) at that time.