Yes, it's possible to match a regex against these strings. Your code can be optimized like this:

open(FILE, "<filelist.txt");
@file = <FILE>;
chomp @file;
close FILE;

open (MYFILE, '>links.txt');
for my $i (1..10) {
 print MYFILE "$file[-$i]";
 print "$1\n" if $file[-$i] =~ m/(\d{8}_\d{4})/;
}
close (MYFILE);
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