Activate only when a monster you control is targeted by a Spell, Trap, or Effect Monster's effect that destroys 1 monster on the field. Switch the target to an appropriate monster your opponent controls.
This card is useless. I put it in my deck specifically to counter dark magician thousand knives card and blue eyes white dragon white lightning spell card. It doesn't work if blue eyes or dark magician are the only monsters on your opponents side of the field when they use the corresponding spell card.
I can see why Burst stream wouldnt work because it doesn't target it just wipes clean. And I could also see Remote Revenge not working if it was a monster destroyed by an effect RANDOMLY. But the fact that Thousand Knives lets you TARGET a monster I control is the 1 and only reason why Remote Revenge should counter it.
There is no appropriate/valid target on the side of the field of the player who activated Thousand Knives, since the player who activated Thousand Knives is not the opponent referred in the card's text.