Its not shot at 18mm, that much is for sure. Going in and looking at similar shots I've done with the kit lens at 18mm, the background stays in focus unless I'm practically shoving the camera down my kid's throat.
My guess is closer to 100mm give or take 50, and standing well back. The closest I'm seeing to how the background looks would be shots I've taken of my kidling either at 65mm f/6.7 with my FA28-90, or 170mm with my Sigma 70-300 at f/7.1. A wide angle THAT close would need to be stopped way, way down on a beach like that which means you'd have practically no depth of field without being so close as to lend screwy perspective to the kids. Also - kids. Grabbing a shot like that would require not being right next to them because they'd be nosy as to whats happening. Its a candid shot, and with children that means not being right next to them where they can wonder who's waving a camera in their faces.
Sigma 70-300 @ 170mm, f/7.1
FA28-90 @65mm, f/6.7