A couple of (tested) minor variations on this solution.

This one mimics your original by avoiding $1:

my %inc = map { my ($v) = $content =~ /inc_$_=(.*?)\n/; $_ => $v }
              qw(albums genres artists songs ratings year);
[download]

my %inc = map { $content =~ /inc_$_=(.*?)\n/ ? ($_ => $1) : () }
              qw(albums genres artists songs ratings year);
[download]

If you want to avoid $1 you can also do it like this (then you don't need a temporary variable):

my %inc = map { $_ => ($content =~ /inc_$_=(.*?)\n/)[0]; }
              qw(albums genres artists songs ratings year);
[download]

Unfortunately, that version does not work in the case of a non-matching regex, producing an invalid hash with an odd number of elements, because a non-match produces an empty list (not undef). It can be fixed with:

my %inc = map { $_ => ($content =~ /inc_$_=(.*?)\n/)[0] || undef }
              qw(albums genres artists songs ratings year);
[download]

Update: The || above should be // to cater for the edge case of "inc_artists=0". Note that the // "defined or" operator was added to Perl 5.10. Note further that the low precedence version of this operator has morphed from err to dor to orelse; orelse is in Perl 6 as a similar but not identical low precedence version of //, but not in Perl 5 AFAICT.

Test program to demonstrate follows. Running:

use strict;
use warnings;
use Data::Dumper;

my $content = <<'GROK';
inc_albums=albumvalue
inc_genres=genrevalue
inc_artists =artistvalue
inc_songs=songsvalue
inc_ratings=ratingsvalue
inc_year=yearvalue
GROK

{
my %inc = map { my ($v) = $content =~ /inc_$_=(.*?)\n/; $_ => $v }
              qw(albums genres artists songs ratings year);
print Dumper(\%inc);
}

{
my %inc = map { $_ => ($content =~ /inc_$_=(.*?)\n/)[0]; }
              qw(albums genres artists songs ratings year);
print Dumper(\%inc);
}

{
my %inc = map { $_ => ($content =~ /inc_$_=(.*?)\n/)[0] || undef }
              qw(albums genres artists songs ratings year);
print Dumper(\%inc);
}
[download]

produces:

$VAR1 = {
          'artists' => undef,
          'ratings' => 'ratingsvalue',
          'songs' => 'songsvalue',
          'genres' => 'genrevalue',
          'albums' => 'albumvalue',
          'year' => 'yearvalue'
        };
Odd number of elements in hash assignment at ff2.pl line 21.
$VAR1 = {
          'ratingsvalue' => 'year',
          'songsvalue' => 'ratings',
          'artists' => 'songs',
          'genres' => 'genrevalue',
          'yearvalue' => undef,
          'albums' => 'albumvalue'
        };
$VAR1 = {
          'artists' => undef,
          'ratings' => 'ratingsvalue',
          'songs' => 'songsvalue',
          'genres' => 'genrevalue',
          'albums' => 'albumvalue',
          'year' => 'yearvalue'
        };
[download]