When I set -Dlog4j.configurationFile=<my-file-path> parameter to JVM args
then the game still uses the default Log4J config.

I checked the command line that started the game and it showed that
in fact the launcher appends this parameter again at the end of all JVM args,
so that the second instance of the parameter overrides my parameter:
... -Dlog4j.configurationFile=<my-file-path> -Dlog4j.configurationFile=<default-file-path> ...

A solution to this problem seems to be simple:
The launcher should append the user's JVM args at the end of all parameters
to allow override any default JVM arg, including overriding the default Log4J config path with a custom path.