How the logs are dealt with is dependant on the operating system and how its configured so the documentation is only able to be general in this case.
For RedHat derived systems which run systemd tyk behaves like a standard systemd started service with messages going to /var/log/messages (assuming default rsyslogd config) as well as being available through journalctl.
This isn’t under tyk’s control, since tyk only logs to stdout and stderr which is why there isn’t a log file option in the config.
There are options to control this in systemd. It might be helpful to have a look at these links
Perhaps an override with something like this would do what you want?