I'm using perl, v5.8.1-RC3 built for darwin-thread-multi-2level, and sometimes the variables do get clobbered (rather than assigned). The explanation you're looking for is that
each array variable is assigned the value ${@_}. BEGIN is called with no arguments, so @_ is empty. ${@_} puts @_ in scalar context so @_ evaluates to the number of its elements, which is 0.

So each array variable is being assigned the value of $0 which is the name of the source file. The while loop reads each line of the source file and sets @_ to the array consisting of that line. At the end of the loop @_ contains only the last line of the file, which evals to 1 and prints the JAPH message as a side effect. The second half of the || should never be executed.

The problem with this explanation is that the order of the variables in %:: is not fixed. Once you set @_ to $0 it is no longer empty, so any subsequent assignments are taken from $1 which is undefined. I've extended your code to print the assignments it's making as they happen: 
LINE: while ( defined( $_ = <ARGV> ) ) {
    @_ = $_;
}

sub BEGIN {
    foreach $_ (%main::) {
        print "\@{$_}='${@_}'\n";
        eval '@{$_}=${@_}';
    }
}
{
    print "Just another perl hacker.\n" unless eval "@_";
}

[download]
I realize this messes up your carefully-designed layout, but eval "}\n" seems to evaluate to a false value, so it still prints the JAPH message. Here's partial output from one less-successful run: 
@{STDIN}='dedalus.pl.tdy'
@{*main::STDIN}='dedalus.pl.tdy'
...
@{_}='dedalus.pl.tdy'
@{*main::_}=''
...
@{ARGV}=''
@{*main::ARGV}=''
...
Can't open : No such file or directory at dedalus.pl.tdy line 1.
Just another perl hacker.

[download]
The following modification of your code seems to work reliably here: 
#! /usr/bin/perl -n
@_=$_}BEGIN{eval'@{$_}=${@_}'for sort keys%::}{eval"@_"||
print "Just another perl hacker.\n"

[download]

In reply to Re^3: A simple JAPH by jdalbec
in thread A simple JAPH by Dedalus

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