KISS no awk:
awk '{for (i=2;i<=9;i++) if ($i != 0) next; n++} END {print n}' file
Perl:
perl -anE '$n += 8 == grep { $_ == 0 } @F[1..8] }{ say $n' file
ou (como sugerido por Glenn Jackman) usando o módulo List :: Util
perl -MList::Util=all -anE '$n++ if all {$_ == 0} @F[1..8]} {say $n' file