It is parsed like this:

#!/usr/bin/perl -w

use strict;
my $key = 'JUMP';

if (
  ($key eq 'ID')
    or ('TITLE')
    or ('GENE')
    or ('CYTOBAND')
    or ('LOCUSLINK')
    or ('CHROMOSOME')
    or ('SCOUNT')
) {
    print "I don't know why this is printing.\n";
}
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and the chain of or's is broken at the first true statement. Namely 'TITLE'. You need to put a lot more "$key eq" statements in there.

The other common options are:

if (grep {$key eq $_} qw(ID TITLE GENE CYTOBAND LOCUSLINK CHROMOSOME S
+COUNT)) {
  print "This didn't print, did it?\n";
}
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or put the list in a hash and write the test as:

if (exists $is_valid{$key}) {
  print "Key '$key' is a valid key\n";
}
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