Bay of Ice reads:
After a player wins initiative, that player kneels all copies of Bay of Ice, then draws a card.
So kneeling the copies is an effect, which means any player can do it. The end result is that, regardless of who controls each copy of Bay of Ice, the player who wins initiative kneels them all and draws a card (unless one or more were already knelt or were prevented from kneeling).
On the other hand, Kingdom of Shadows reads:
After a player wins an INT challenge, that player kneels all copies of Kingdom of Shadows to choose and stand a card with the SHADOW crest.
So kneeling the copies is a cost, which means only the controller of each copy of Kingdom of Shadows may kneel it (since you can pay costs only with cards you control). The end result is that only a player who controls all copies of Kingdom of Shadows can kneel them all to pay the cost. Once multiple players control a copy of it, no one can get to choose and stand a card with the SHADOW crest and a player who doesn't control a copy will never get to stand a card with the SHADOW crest.
Is this what was intended? Or should Kingdom of Shadows be worded like Bay of Ice?