Sides on the box/tray aren't a requirement, ledges in the wild do not have edges after all. Alot of the boxes with webcams are build up high and affixed to something so the edges are an added precaution to protect the chicks and to provide the adults and young with an edge to hang onto. Imagine the Elk River box, you are either in the box or on the bars/frame attached to the box. On the Radisson, though we have a ledge the chicks use as a runway, our box is narrower than many others so we have sides to protect them if they get too curious/adventurous. At the Maine site, the box is in a niche, so the chicks when they get big enough to want to wander off the gravel (> 3-4 weeks of age) they are still protected as the niche has walls on at least three sides - so think of the walls around the nest tray as really (really) high tray edges. A similar tray is in use at the Hamilton, Ontario nestsite if you want to check out the design in a differend environment.
The chicks and the adults will be fine. The gravel will help the adults to keep the eggs in place for incubation and the chicks won't be nearly mobile enough to go anywhere until after banding age (3+ weeks). After that, the chicks don't need the adults protection from the weather and it won't matter if they stay together on the gravel.