Your php-fpm.conf file is not set up to send errors to syslog. See below for an example of how to do this.
; Error log file
; If it's set to "syslog", log is sent to syslogd instead of being written
; in a local file.
; Note: the default prefix is /var
; Default Value: log/php-fpm.log
error_log = syslog
; syslog_facility is used to specify what type of program is logging the
; message. This lets syslogd specify that messages from different facilities
; will be handled differently.
; See syslog(3) for possible values (ex daemon equiv LOG_DAEMON)
; Default Value: daemon
;syslog.facility = daemon
; syslog_ident is prepended to every message. If you have multiple FPM
; instances running on the same server, you can change the default value
; which must suit common needs.
; Default Value: php-fpm
;syslog.ident = php-fpm
; Log level
; Possible Values: alert, error, warning, notice, debug
; Default Value: notice
;log_level = notice