See this answer and the posts here. For more background visit mdn.
Essentially you're running into a security issue where the browser won't allow you to make a request from http://local.mysite.com
to http://api.steampowered.com
.
Do you have access to a server? Instead of making a request like this: browser -> steampowered
you can make a request like this browser -> your server -> steampowered
.
You're going to want to create an endpoint on your server (so that it's in your domain) that you can send a request to, that will in turn send a request to steam powered.
What language / framework are you running and we can give you example code.