I know this is an old question but as I was lurking around these parts on this exact topic... here's my take:
From what I can see, the resource text file is being treated as a text file where it is hoped File.ReadAllLines(Conundrum.Properties.Resources.Words) would read the lines within the .txt file as strings.
However, by using ReadAllLines() this way, it immediately reads the first line as the filepath name, hence the error message.
I suggest adding the file as a resource as per this answer from @Contango.
Then, as per this answer from @dtb, with a little bit of modification, you will be able to read the text file contents:
        using System.Reflection; //Needs this namespace for StreamReader
        
        var assembly = Assembly.GetExecutingAssembly();
        
        //Ensure you include additional folder information before filename
        var resourceName = "Namespace.FolderName.txtfile.txt"; 
        using (Stream stream = assembly.GetManifestResourceStream(resourceName))
        using (StreamReader sr = new StreamReader(stream))
        {
            string line;
            while ((line = sr.ReadLine()) != null)
            {
                //As an example, I'm using a CSV textfile
                //So want to split my strings using commas
                string[] fields = line.Split(',');                  
                
                string item = fields[0];
                string item1 = fields[1];
            }
            sr.Close();
        }