The problem is probably in your conditionals; $command == 'start' compares $command and 'start' as numbers, likely converting them both to zero first then finding them always equal. You probably meant to use $command eq 'start', etc.

You may find it useful to switch to a dispatch table instead of a whole bunch of if statements:

sub handle_start {
  my($client,$param) = @_;
  print $client "Welcome to the game: $param\n";
}

# ... more commands ...
my %commands = (
  start   => \&handle_start,
  # ... more ...
);

sub handle {
   # ...
   if (not exsits $commands{$commands}) {
     # bad command
   } else {
     # run command
     $commands{$command}->($client,$param);
   }
   # ...
}
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(A side note: split always treats it's first argument as a regex, even if it is single-quoted like you have it. As a matter of style, I would advise using /<div>/ or similar so as not to make it look like it doesn't take a regex...)