This site reaches out to instagram for the first 20 or so posts and displays them in a grid. You can pull up the modal by clicking on one of the thumbnails. Videos have a video icon in the top right corner.
As you scroll down the page you will see a loading indicator, once you see this, the page reaches out to instagram and loads the next 20 until there are no more posts from him.
I decided to use hyperapp js library which I was drawn to after looking through the github repo. It has a simple state, actions, and view management which allowed for a very smooth development.