Here is what I would do...
I would start over from scratch
Uninstall everything and reinstall it
I would not enable any modules
I would then run the test config and test output commands on filebeat to make sure filebeat.yml works The config is correct and it can connect to elasticsearch.
See command here
Then in the filebeat.yml I would enable that top filestream and just put a log file somewhere and have filebeat read it... It will only read it once, so you'll need to add more lines if you want to see more.
Once you get all that working then I would try the system module... just enable syslog and put your paths, don't move it, don't add anything else to it like the file you showed above... (seems like you are reading somewhere that you can combine them... which you can if you are advanced user but I would get the basics working first)
That would be my suggestion
There are also troubleshooting and debug help in the docs.