It is because you are only applying the map to the first line of the file. Try:

use strict;
use Data::Dumper;
my %hash;
%hash = map {map { chomp; $_ => '1' } split /(\s+|\W+)/} <DATA>;

print Dumper(\%hash);


__DATA__
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MY BIG TOE
BOOK 1:
A WAKENING
Section 1
Delusion or Knowledge:
Is This Guy Nuts, or What?
Section 2
Mysticism Demystified
The Foundations of Reality
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The My Big TOE reality model will help
you understand your life, your purpose,
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