Some rcon clients logs the chat by detecting the output type as chat. Adding the following after Puts at the bottom of OnServerCommand adds support for this. 

ulong userid = 0;

if (player != null)          
userid = player.userID;
            
ConVar.Chat.ChatEntry rconchat = new ConVar.Chat.ChatEntry
{
    Message = string.Join(" ", arg.Args),
    UserId = userid,
    Username = _config.Title,
    Color = _config.MessageColor,
    Time = Facepunch.Math.Epoch.Current
};

Facepunch.RCon.Broadcast(Facepunch.RCon.LogType.Chat, rconchat);​

That would be something to add in Oxide/uMod for Rust, not necessarily this plugin.