I had a different take (that makes minor changes to your solution). I thought he wanted non-subsets within each seq identifier, (where your solution finds them for the whole file not considering the first column).

I added 2 more lines to the for loop and 1 more line to the sorter sub.

#!/usr/bin/perl
use strict;
use warnings;
use 5.010;


open my $fh, '<', \<<EOF;
SEQ1 225 275
SEQ1 200 300
SEQ1 201 299
SEQ1 250 399
SEQ1 145 244
SEQ2 120 130
SEQ2 100 150
SEQ2 101 149
SEQ2 120 230
SEQ2 99 140
EOF

my @terms;
while (<$fh>) {
    chomp;
    push @terms, [split /\s+/];
}

my $biggest = 0;
my $id = '';
for my $term (sort sorter @terms) {
    $biggest = 0 if $id ne $term->[0];
    if ($term->[2] > $biggest) {
        say join ' ', @$term;
        $biggest = $term->[2];
    }
    $id = $term->[0];    
}

sub sorter {
    $a->[0] cmp $b->[0] ||
     $a->[1] <=> $b->[1]
  || $b->[2] <=> $a->[2]
}
[download]

The output is:

SEQ1 145 244
SEQ1 200 300
SEQ1 250 399
SEQ2 99 140
SEQ2 100 150
SEQ2 120 230
[download]