There was a lot of activity in the late ‘90s around what “authentic to the medium” web design could look like, but I don’t remember people being very interested in emulating traditional print design — which itself was in turmoil thanks to digital publishing systems. Open a 1996 issue of Wired and you’ll probably think the designers were on crack: purple text on garish background images, cut-up barely readable fonts, that kind of thing.
Some other smaller things also contributed but I don't think they were such big deals:
- Lack of good compression on both transfer of data and file formats, necessitating simpler designs and palette-based image formats.
- Graphics acceleration was generally slow so smooth animations were out.
- Image creation/editing tools were practically non-existent and digital cameras were rare so it makes sense that the resulting pages that have had designed assets were scary-looking.