Replacing broken links is almost always a good thing. A broken link has no value, so changing it to point to something relevant is always a net positive. If a new link target can be found with the same text that is quoted in the post, there is no downside to the change. This can be accomplished by finding a new version with the same text, as the linked change does, or by finding the same content on a different site, or by linking to a copy of the original content using the Internet Archive's Wayback Machine.
There may also be value in updating rules links to point to newer versions of the rules, whether or not the existing link is broken. The best way to handle this depends on how the relevant rules sections have changed:
If the current rules contain the same text that is quoted in the post, any user can edit to replace the link with the newer one. It is generally more helpful to readers to show that the answer applies to the current rules than to show that it applies to some specific past version of the rules.
If the current rules contain different text that does not materially change the answer, any user can edit to replace the link and the corresponding quotation.
If the current rules contain different text that invalidates or materially changes the answer, only the user who wrote the post should make the change. Any other user should go through the normal process of making a material factual correction to a post: make a comment on the answer describing the correction and/or post a new answer with the correct information.
Now, whether these changes should be made at all may depend on community norms for the specific game. In Magic: the Gathering, new rules always supersede old ones, so any answer that is invalidated by new rules is simply incorrect, and should be changed as soon as possible. Other games may have independent version-specific rules. Those should already have version-specific tags, and when making edits users should make sure not to change what version of the rules they reference.
In the first two cases, if the link is not broken, these changes may not be substantial enough to justify an edit, though making those changes is perfectly valid if the answer needs other edits too. In particular, when a new version of a rulebook is published you should not edit every answer that references the rulebook to point to the new version.