manually rotating logfile with rsyslogd

You don't tell logrotate which file to rotate on the command line. You pass it a configuration file. So in your case, logrotate is reading /var/log/syslog and trying to parse it as a config file and failing (hence your errors).

If you want to rotate /var/log/syslog it needs to be listed in a logrotate config file somewhere, and you just run logrotate. If it rotated recently, then logrotate -f to force it to do it again.

Here's an example entry for /var/log/syslog from Debian,

/var/log/syslog
{
        rotate 7
        daily
        missingok
        notifempty
        delaycompress
        compress
        postrotate
                invoke-rc.d rsyslog reload > /dev/null
        endscript
}

So, you need that in a file, normally either /etc/logrotate.conf or as a file snippet in /etc/logrotate.d assuming your /etc/logrotate.conf points there, and then you just run logrotate /etc/logrotate.conf.

Since you're running Debian, this is probably all in place, and all you need to actually do is run logrotate -f /etc/logrotate.conf (note, this will rotate every log currently configured in logrotate).

If you truly only want to rotate /var/log/syslog, you will need to create a config file that just does that one log, based on the content of /etc/logrotate.conf + /etc/logrotate.d/rsyslog.