The answers to your question is "It depends."
It depends on your new scoring mechanism.
The scoring mechanism for King of the Hill challenges is not implied.
If you convert a code-golf challenge to a king-of-the-hill challenge where the winner is the submission with the shortest code, then you have not only misunderstood the purpose of the King of the Hill tag, but you have not changed the challenge at all. I would vote to close it.
If you convert a code-golf challenge to a king-of-the-hill challenge where the winner is the submission with the most wins after some series of random or round-robin pairings or free-for-alls, then you have completely transformed the type of answers you are likely to get. I would not vote to close it.
It depends on who you ask.
The answer is subjective. Doorknob quoted a commonly accepted rule that attempts to remove some of the subjectivity:
Could answers from the previous question be reposted in your new one?
You pass that test. But I don't like trying to hammer subjectivity out of a community vote that is based entirely on subjective reasons. Here's my rule:
Does the question add value to the site?
In the specific case of a Connect 4 KotH challenge, I feel that challenging users to build bots that aim for optimal play rather than shortest code adds significant value to the site, and so I would not vote to close.