The downloads you can retrieve from wikia are database dumps. In order to make use of those, you would have to install your own local instance of Mediawiki, with a database server and web server to run it. If you're looking to do that for Paragon Wiki then no, we don't have an option to download database dumps. However, you can export the equivalent data for articles of your choosing using
http://paragonwiki.com/wiki/Special:Export and then import that data on your wiki using Special:Import.
However, be advised that Paragon Wiki uses a bunch of extensions. The pages you import are likely to be broken if you don't set everything up right. Morever, we use DPL and SMW extensively. Pages that use DPL or SMW queries won't work unless you copy over all the articles the depend on.
That's a lot of work, and it only gives you the text content (same as with Wikia). You won't get any images that way; you'd have to do those manually (same as with Wikia).
If you just want a local copy for browsing purposes, then
HTTrack is likely a better option. But be aware that it's going to be in the ballpark of 4 GB of data to download, thanks to the images.