That game site is called Freebie Games.
The link is https://freebie.games/
They keep the ROM with them so they don't break any copyright laws where they are located. You don't need to install anything to play the games, you just need a working web browser that supports their technology.
I found it also generates the controllers needed to run the game. I managed to find my favourite dos game on there and play it on my smartphone using the little controllers that it provided.