@ARGV would be an Array with four entries like this right?

Yes, except for the new lines, \n. Prove this to yourself with a test script:

use strict;
use warnings;

print "These are the ", scalar @ARGV, " arguments:\n";
my $i = 0;
for (@ARGV) {
    print "ARGV[$i] = $_\n";
    $i++;
}
[download]

prints:

These are the 4 arguments:
ARGV[0] = s/foo/bar/
ARGV[1] = file1.txt
ARGV[2] = file2.txt
ARGV[3] = file3.txt
[download]

Alternately, you can use Data::Dumper:

use strict;
use warnings;
use Data::Dumper;
print Dumper(\@ARGV);
[download]

prints:

$VAR1 = [
          's/foo/bar/',
          'file1.txt',
          'file2.txt',
          'file3.txt'
        ];
[download]

What I do not understand is how the script determines which files to put into @ARGV. At which point is "*.txt" being evaluated? Or is it the shell that tells the script which files in the directory match the pattern *.txt?

The shift built-in function removes element 0 from the @ARGV array, shifting the remaining elements [1:3] down to new positions [0:2]. Again, here is a simple test script:

use strict;
use warnings;

my $op = shift;
# same as: my $op = shift @ARGV;

print "These are the ", scalar @ARGV, " arguments:\n";
my $i = 0;
for (@ARGV) {
    print "ARGV[$i] = $_\n";
    $i++;
}
[download]

prints:

These are the 3 arguments:
ARGV[0] = file1.txt
ARGV[1] = file2.txt
ARGV[2] = file3.txt
[download]

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