Trouble getting json back

Question

Assuming the first code you show is in the file (incorrectly) named "gameData.json", what you're trying to parse isn't JSON (or JSONP), it's plain JavaScript.

So don't parse it.

Change

var obj = $.parseJSON(jsonp);

to

var obj = jsonp;

Notes :

JSON is a text based data interchange format. Your confusion might come from the many young developers using non-sensical expressions like "JSON object"...
You should avoid naming jsonp a variable holding a plain JavaScript object.

If you prefer to load a JSON file instead of executing a JavaScript file, then

remove the "jsonp = part to make it a real JSON file
remove the script element (as it's not JavaScript anymore)
load the JSON file using ajax

Here's how the JavaScript would be like :

$(document).ready(function() {
   $.getJSON("gameData.json", function(obj){
      $.each(obj, function() {
          alert(this['gameImage']);
      });
   });
});

or, if you can afford not supporting IE8 :

$(document).ready(function() {
   $.getJSON("gameData.json", function(arr){
      arr.forEach(function(item){
          console.log(item.gameImage); // yes, prefer the console over alert
      });
   });
});