Bush is in charge of the executive branch of government at the current time, his main competitor for the job when the vacancy came up, Gore, would have used executive orders to fulfill his pet project called the Kyoto treaty.
So, IMO, Bush did kill Kyoto by defeating the main supporter of Kyoto, Gore, and not putting out executive orders fulfilling Kyoto as Gore would have done.
I'm sorry, but it is just "here" where he gets the "credit" for killing Kyoto but the world over with much gnashing of teeth.
Never mind the Senate vote of yore, politically it is George Bush who drove the stake through its heart.