If the first link style is working, then you already have the rewrite rules you need -- it appears to be a XenForo site where all non-existing routes are sent to index.php.
In order to be able to process the latter form of links, the wiki needs to be configured to use that URL format in the AdminCP > Home > Options > VaultWiki: Site Config > Wiki URL Format. If you prefer the first form, then you will need a rewrite rule to turn the second form back to the first form, and that should be easy.
Code:
location ~ ^/wiki/.+ {
rewrite ^/wiki/(.+) /wiki/?title=$1&$args permanent;
}
If, after activating the second format, the first format does not forward to the second format, that is a bug.