Short answer

While it's possible to use files stored in Google Drive as website resources at this time it's not officially supported and should not be used for websites and spreadsheets that have a lifespan beyond August 31, 2016.

As was mentioned by AE I in his answer to a related question, the use of https://docs.google.com/uc?export=view&id=FILE_ID is not documented and could stop to work at any time without previous official notice but at this time (February, 2019) it still works.

Explanation

The instructions to publish Google Drive files as website content are in Publish Website Content - Google Drive REST API but according to Deprecating web hosting support in Google Drive - Google Apps Developer Blog

Beginning August 31st, 2015, web hosting in Google Drive for users and developers will be deprecated. You can continue to use this feature for a period of one year until August 31st, 2016, when we will discontinue serving content via googledrive.com/host/[doc id].

I modified the script so that it accepts arrays of column headers:

• updateColNames lists the columns that you want to keep track of
• timeStampColNames lists the columns where timestamps should appear, in the same order.

There is now a for loop that goes over the tracked columns one by one, comparing them to the edit location, and inserting timestamp when needed.

I also changed the handling of sheet name, because the original version appeared to edit the sheet named Feb 16 regardless of where the edit was.

function onEdit(e) { 
  var timezone = "GMT-5"; 
  var timestamp_format = "MMMM-dd HH:mm"; // Timestamp Format. 

  var updateColNames = ["Student First, Last Name", "Another Column to Watch"]; 
  var timeStampColNames = ["Name Timestamp", "Another Timestamp"]; 

  var sheet = e.range.getSheet();
  if (sheet.getSheetName() == 'Feb 16') {    // Name of the sheet to track

    var editColumn = e.range.getColumn(); 
    var row = e.range.getRow(); 
    var headers = sheet.getRange(1, 1, 1, sheet.getLastColumn()).getValues(); 

    if (row > 1) {
      for (var i = 0; i < updateColNames.length; i++) {
        var dateCol = headers[0].indexOf(timeStampColNames[i]); 
        var updateCol = headers[0].indexOf(updateColNames[i]) + 1;  
        if (dateCol > -1 && editColumn == updateCol) {
          var cell = sheet.getRange(row, dateCol + 1); 
          var date = Utilities.formatDate(new Date(), timezone, timestamp_format); 
          cell.setValue(date); 
        }
      }
    }
  }
}