"Heavy Rain" was unique in the gaming world, but "LA Noire", "Beyond Two Souls," "Hotel Dusk Room 215," and "Walking Dead" episodes are all similar. Each of these games offers a style, tone and variety of choice similar to those of "Heavy Rain."
"Heavy Rain" was the first to offer gamers so many different possible paths for the story line. Every decision made during gameplay has an impact on the direction that the story takes. This means the game has more than a dozen different endings, each with specific requirements to see it.
The level of difficulty in creating numerous different scenarios had discouraged many game developers from attempting to make a game similar to "Heavy Rain." That is why there were so few examples of games similar to it. It wasn't until the advancement in the power of gaming consoles and PCs that other games like "Heavy Rain" became feasible for game developers.
Many developers have either broken up the games into different episodes or toned down the number of possible outcomes. In the case of episode games, developers have more time and space to create the different outcomes and develop the heavy tone and style that games like "Heavy Rain" require.