Tell me this: at what point does $cfg get a value from &Config::Simple::new when the program is requested to load a game via load game string coming in from STDIN?

Between declaration of $cfg variable on line 31 and call to &load_game sub on line 83, $cfg remains undefined. And, what is very first statement of &load_game? It is a call to a(n) (unknown) method read on yet-to-be-defined $cfg. That is the reason for the error message.

$cfg needs to be defined (even) in &load_game sub before a method could be called on it, much like in the first statement of &new_game sub on line 107. You can do one of at least two things ...

sub load_game {

  #  No need for separate "$cfg->read( ... )".
  $cfg = Config::Simple->new( 'file' );
  
  #  or ...

  $cfg = Config::Simple->new;
  $cfg->read( 'file' );

  ...
}
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Note that the solution in both forms is already presented in "READING THE CONFIGURATION FILE" section of pod.