... This, however, doesn't parallel Perl's documentation. Am I doing something stupid? Is Perl's documentation wrong? Are we both wrong?

You're wrong because you're taking an analogy past its limits, ignoring documentation in the interim.
`perldoc -f map'

Evaluates the BLOCK or EXPR for each element of LIST (locally setting $_ to each element) and returns the list value composed of the results of each such evaluation...

    %hash = map { getkey($_) => $_ } @array;
[download]

is just a funny way to write

    %hash = ();
    foreach $_ (@array) {
        $hash{getkey($_)} = $_;
    }
[download]

The assignment operator (which is discussed through out the perl documentation) is waiting for map (a list operator) to return a list, before it can proceed with the assignment. To get

  my %res = map {
    $_ => do {
        my $re;
        $re .= $translations{$_} for split //;
        $re;
    } if !$res{$_};
  } @words;
[download]

to work as you intended , you need to change it to

  my %res;
  my @res = map {
    $_ => do {
        my $re;
        $re .= $translations{$_} for split //;
        $re;
    } if !$res{$_};
  } @words;
  %res = @res;
[download]

update: or even

  my %res;
  %res = @_ =map {
    $_ => do {
        my $re;
        $re .= $translations{$_} for split //;
        $re;
    } if !$res{$_};
  } @words;
[download]

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