Thanks for attaching configmap and deployment yaml. Can you try below config.

From Parser Plugin Overview. They provided a simple example to get nginx logs.

<source>
  @type tail
  path /path/to/input/file
  <parse>
    @type nginx
    keep_time_key true
  </parse>
</source>

Can you add above config in configmap and try. The nginx parser is in-built, the link you provided is explanation of parser internals. If you don't like the way it is selecting/parsing, you can write your own.

Anyways, by using @type we can define type of parser we want.

PS: Right now I dont have any setup to test this. Also I have little knowledge in fluentd

EDIT:

I believe you already knew how fluentd is getting logs... In your pastebin link, at volumeMounts section, it mounting host's /var/lib/docker/containers which has all container meta data and logs, etc