Sorry, I couldn't understand you.
Does it just terminate without any output when you run it, or the shell tries to make you input some more text? Can you show the exact command you run (you said that you tried passing the filename as a commandline argument, which is right)? What shell are you using? Can you show a small example of file being parsed?
You can also put the whole oneliner in a file, like this:

#!/usr/bin/perl -n
# note the -n switch
use Date::Parse;
use features 'say';
BEGIN{$main::now=time;$main::old=(time-60*10)}
if(/^(\w+\s+\d+\s+\d+:\d+:\d+)/) {$t=str2time $1; $t > $old && $t < $n
+ow && print}
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And then run it passing file names as a command line arguments (perl script.pl my_log_1.log my_log_2.log) or feeding them to STDIN (cat my_log_*.log | perl script.pl).