I think that "on" is acceptable. I've also seen "broken link to". I'm not sure which one is correct in your case. Perhaps we need the context to decide.
Anyway, a moderator will problably solve the problem.
You may say «there is a broken link on the Computer Game website». The link is then on the Computer Game site.
You may also say ««there is a broken link to the Computer Game website» or «the link to the Computer Game website is broken». The link is then on another website.