I'm trying to retrieve some old package files off Wayback, e.g.

http://rapidgator.net/file/3c7fa590...KAM1E1.rar.html

As the link is broken, and I have the name of the package file, e.g. WA2015BECKAM1E1, is there any way I can download the file some other way?

It is impossible to download a file without a working link, no exceptions. The reason the link is broken is usually because the file isn't on that host anymore, and you cannot download a file that isn't there.

However, there are a number of ways that it is sometimes possible to find a new, working link for a file even though the first link you found was broken. Knowing the filename is one of the ways you might be able to do it, but not usually the most useful. Including more info (creator name and item name, the exact URLs of the dead webpages you were accessing in Wayback, etc.) might allow someone else to find a working link for your item if you're not sure how to look for one yourself.

I know the creator and the item name and have scoured every inch online for any links I can find. But they are all broken and the creator is no longer active. Thanks for the information in any case.