I'm guessing you are looking for the genes for a certain id, and then a looking for all the id's that have those genes. If so try this

#!perl
use strict;
use warnings;
my $match = 'DOID:2055';
   
my $filename = 'do_human_mapping.gmt';
open (my $fh, '<', $filename) or die "open: $!";
my @genes=();
my %gene2id=();

while (<$fh>){
  my ($name,$id,@temp) = split /\s+/;
  if ($id eq $match) {
    @genes = @temp;
  } else {
    for my $gene (@temp){
      push @{$gene2id{$gene}},$id
    }
  }
}

for my $gene (@genes){
  if (exists $gene2id{$gene}){
    print join ' ',$gene,@{$gene2id{$gene}},"\n";
  }
}

__DATA__
 DOID:00001 APOE IL4 RTG5
 DOID:00002 FG6 CRH APOE
 DOID:00003 RTG5 HUTN CRH
 DOID:2055 APOE FKBP5 CRH
[download]

poj