The problem is that you get the current class logger in the LogListener:
private static readonly NLog.Logger Log = NLog.LogManager.GetCurrentClassLogger();
That way, you always log to the NLogListener type. What you should do is get the right logger type for each entry:
protected override void Debug(ILog log, string message, object extraData)
{
var nlog = NLog.LogManager.GetClassLogger(log.TargetType);
nlog.Debug(message);
}