Using @push does not maintain the correct column alignment. You need to assign values to the element associated with that file number.

#!/usr/bin/env perl
use strict;
use warnings;
my %data = ();

#@ARGV = map { "File$_" }(1..4);
my $num = @ARGV;

# input
for my $i (0..$num-1){
  open my $fh,'<',$ARGV[$i] or die "$!";
  while (<$fh>) {
    my ( $key, $value ) = split;
    $data{$key}[$i] = $value;
  }
  close $fh;
}

# output
print join ("\t", 'ID', @ARGV),"\n";
foreach my $key ( sort keys %data ) {
    my @line = map { $_ || '-' } @{ $data{$key} }[0..$num-1];
    if (grep $_ eq '-',@line){
      print join ("\t", $key, @line),"\n";
    }
}
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