The [] brackets are used to create a list reference. A reference is a scalar ($ sigil), not an array (@ sigil). To understand references, have a look at perlref. You could get it to work by dereferencing the $compass reference, like this:

#!/usr/bin/perl
use strict;
use warnings;
use Data::Dumper;
my $compass =
    [
       ["NW", "N", "NE"],
       ["W", "center", "E"],
       ["SW", "S", "SE"]
    ];
print Dumper($compass);
print $compass->[0][1];
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