No, chomping @ARGV is not necessary. The shell already splits command-line arguments by whitespace, and removes said whitespace (note that Athanasius talks about chomping lines from the file, not from @ARGV).
Also, you're using two-argument form of open. The Perl's documentation says:
The filename passed to the one- and two-argument forms of open() will have leading and trailing whitespace deleted and normal redirection characters honored. This property, known as "magic open", can often be used to good effect.
You normally don't actually want Perl to be overly 'magical' with some redirection characters that might end up in filenames somehow; nor do you want it to chomp filenames automatically (if there is whitespace in @ARGV, the user made it so, and he probably knows why arguments must contain whitespace). It is best to use three-argument form of open:
open my $INPUT_FILE, '<', $DNA or die;
