What you've got there is pretty close, but you've got the syntax for the push part a bit backwards. With push, you always specify the array to be pushed onto first, and you don't use the assignment operator:

my %hash;

foreach my $ary ( @array ) {
        if ( !defined($$ary[1]) ) { $$ary[1] = '0' }
        push @{$hash{$$ary[1]}}, $$ary[0];
}
print Dumper \%hash;
[download]

I also changed your @$ usage to $$. @$ary[1] is an array slice, which is not appropriate to use when you are only dealing with single elements, as is the case here. I also introduced the defined function, which is the only valid way to check whether a value is defined or not (string comparison to undef will succeed for the empty string '' and throw a warning).

By the way, as a personal preference I like to use -> for single element lookups in hash or array references because I think it is clearer. So everywhere you have $$ary[1] you can instead say $ary->[1].

Forgot one other thing. I changed print Dumper %hash to print Dumper \%hash because otherwise Dumper will treat your hash as simply a list of values and not as an actual hash.

Yet one more. I aligned the two statements inside the foreach loop because they are in fact part of the same block. In the OP a reader might think that push statement was part of the if block, which it's not.