for short: the split accepts a regexp as first parameter, wherein the | is a metasymbol, and you did NOT quote it properly ... ;)

use strict;
use warnings;

use constant FIRST_FIELD => 1;
use constant SECOND_FIELD => 2;
use constant THIRD_FIELD => 3;

my $str = "";
{ local $/; $str = <DATA>; }

$str = join "\n",    map { $_->[0] }
                    sort {$a->[THIRD_FIELD] cmp $b->[THIRD_FIELD] }
                    map { [$_, split('\|', $_)] } split(/\n/, $str);

print $str;

__DATA__
xyz4|1026|CR
xyz3|3461|CR
dert5|3251|PR
rtyaq|251|PR
dbca|583|PR
xxxt|360|CR
[download]

note further that cmp does NOT work for numerics, or look for yourself what is going wrong :) you need the <=> operator to do numeric sorting in this way.
and you saw the characters "ST" or "schwartzian transform" along with the code? ;)
HTH

UPDATE: added ST line