Everything feels wrong with that approach too me, starting with calling a perfectly time-appropriate website anachronistic.
Anachronistic would be something like creating an apparent flash website for a fictional 90s internet related movie.
He's using it correctly, in its secondary sense of "belonging or appropriate to an earlier period, especially so as to seem conspicuously old-fashioned or outdated."
He's using it correctly, in its secondary sense of "belonging or appropriate to an earlier period, especially so as to seem conspicuously old-fashioned or outdated."