I read the sentence a couple of times to try to figure out what the phrase “ephemeral gauze” was intended to convey but failed to make sense of it. So, I figured that “gaze” may have been the intended word, i.e., readers pay particular attention to text while they’re in the process of reading it (gaze) but that it’s quickly forgotten when they move on to the next unrelated thing they see on the Internet (ephemerality).

I’m only familiar with gauze in the context of first-aid kits and other medical usage so I’d appreciate hearing your interpretation of “ephemeral gauze”.

As opposed to the solid materiality of books, the "material" of the internet is an "ephemeral gauze", a thin and shifting fabric (a mesh, literally a web) on which it would be impossible to apply ink, to hold rigid, etc.