I've seen other people making these in After Effects 3D environments with camera moves, but this is faux 3D.

I separated elements of the photo into Photoshop layers, extending the textures of each layer slightly behind the next. Then in Final Cut, each layer is slightly scaled up with varying levels of gauzian blur and then moved at different rates from one side of the screen to the other.

It's four layers: The deck, the DJs, the crowd and the room.