As different to "normal" folk? Is it so because of "dirty" sounds? Example
"Dirty folk" does not seem to be a term in wide or common use. The "dirty blues", however, is an old and well-established subgenre of the blues. It is called "dirty" because it has "dirty" words and/or sexual themes. Based on the link you provided, "dirty folk" is likely the same thing for folk music --folk music with bad language and/or sexual themes.
An alternate interpretation would be, as you suggested, folk music with a "dirty" audio quality, but this would more likely be called "gritty", "lo-fi" or "indie" folk. (The link is somewhat ambiguous because it compiles songs from four separate genres.)
Either way, there is likely some overlap with "anti-folk" which is a low-fi folk subgenre with contemporary, often explicit language and themes.