XML dumps are required, as to import an older mediawiki's SQL requires significant expertise with My SQL etc.
To restore an old SQL version, it's best to install the original mediawiki it was for, restore the database in phpmyadmin, and then forward-upgrade the code.
For larger PHPWikis, Isaac Wilcox has written a Perl script to do the conversion.
Use Mod Wiki is a Perl script which uses a database of text files to generate a Wiki Wiki site.
It usually runs as a CGI script in response to web requests, but can be called directly by other Perl programs.
With tens of millions of some of the most heavily accessed & trusted content in the world already in mediawiki format, it is generally up to those maintaining data in incompatible formats to make it accessible in mediawiki, not the other way around.
Mediawiki is focused on presenting its own wikitext effectively & in every language and device, it is fundamentally not focused on old or obsolete database import.
Jamwiki stores data in a variety of forms including flat file.
Converting a Jamwiki database to flat file should produce entirely compatible pages to mediawiki, which can be uploaded with any bot script or manually, since the format is identical to mediawiki's Mediawiki's wikitext markup is by far the most commonly used in the world & supports by far the most natural languages & character sets.There is at present no facility for current mediawikis similar to the old Get Wiki 1.0 live XML importing which mirrored another (usually Wikipedia) mediawiki & used its page content as default unless edited at the new (mirroring) mediawiki.This feature however can be weakly simulated with frequent import of XML dumps for pages that don't exist on an importing wiki, ignoring versions of pages that do or over-writing them from a backup just prior to importing the XML dump.A riskier method is to install a new mediawiki, rename its database in phpmyadmin, import the older one, rename it to match the name used in the newer install expected in its code, and carefully restore priveleges from the renamed DB to match.Then run mw-config update (not the maintenance script, it may not work) and export the mediawiki to XML properly as backup.Availability of wiki farms (wikia, refarata, etc), bitnami installers, pre-configured cloud images, good wiki-based support on shared hosts (especially Dreamhost), more powerful desktops & LAN servers, and improved XML based backup & restore tools, have made it possible to maintain a mediawiki without special expertise, obsoleting most other wiki.