The answer isn't worse because it only applies to older version of Chrome. The question doesn't specify a Chrome version, so answers for any versions are equally valid. It's not either user's fault that the versioning scheme of Chrome makes it impossible to tie questions to versions, like we'd do with e.g. windows-xp.
I don't think downvoting is the way to go here. We wouldn't downvote a late answer that only applies to older software versions either (something that should be actively encouraged! It's often the older versions of software that require the tricky workarounds). The only difference would be that the later poster can already know for which more recent software versions his solution will not work anymore.
The answer has a built-in warning sign in the date and time it was posted (Chrome + 3 years old information = irrelevant), and it's possible to sort answers by date, allowing readers to start at the most recent ones (admittedly at the bottom).
Instead you should edit the answer to provide more information about the assumptions of the answer ("In Chrome N.0 and earlier, ...") or add a comment stating "As of version N, this answer no longer applies". This way, readers will be able to quickly determine which of the answers applies to their situation.
The more recent answer should rise to the top over time anyway, as future readers will find it more relevant.