I think this will do what you want.

use strict;
use warnings;

use YAML;

my %hosts;
my $current_host;
while ( my $line = <DATA> ) {
    chomp $line;
    if ( my ($host) = $line =~ /\[(\w+)\]/ ) {
        $current_host = $host;
        push @{ $hosts{$current_host} }, $host;
    }
    elsif ( my ($dir) = $line =~ /"([^"]+)"/ ){
        push @{ $hosts{$current_host} }, $dir;
    }
}

print Dump \%hosts;

__DATA__
[msservername1]
"/etc/like"
"/etc/whatever"
[msservername2]
"/etc/whatever"
__END__
---
msservername1:
  - msservername1
  - /etc/like
  - /etc/whatever
msservername2:
  - msservername2
  - /etc/whatever
[download]

I don't put the result in @mshost1, @mshost2 etc since I don't know how many there will be and it is bad practice to generate them on the fly. Instead I've put them in a hash keyed on the host name.