There's at least one Nginx connector in the LEM, not sure if that relates to the same logs you're looking for or not, but you may want to start there. It would be set up on a Linux based server to read the data directly with the agent typically.
Otherwise you're likely right that you will need to reach out to support to see if this will be a connector request. With a sample of the log data they can help you find an existing connector if one will match, but there aren't really any supported generic syslog connectors.
One was created once upon a time and made available on Thwack, but it is not supportable and not the best way to bring data into the LEM (it isn't going to normalize the data really for use in rules and reports):