I would agree that level design is not only visual, but more like stage design as it is creating an environment which characters can interact with, but only what is available to the players. During my attempts at level design in previous years the key thing is that you as the designer have to think about the limitations of the game engine, for example having a large area where every single side of the models have a texture on where you wouldn't necessarily see or want the players to be able to see is more cost effective to frame rate and general compatibility.
Like in stage design there are many things in the background, underneath the simulated floor boards and walls/environment which are not meant to visible to the audience, but can aid in keeping the environments/props up. With the engines iv been using the way which you can reduce frame rate, rather than drawing every side(even if meant not to be seen) is by using shaders - known as the CAULK shader as seen here: http://www.richdiesal.map-craft.com/tutorials/gc102lsn1.html
Basically a texture is applied to a mesh or a model and then you select the areas of the model which are not to be seen by the players and apply this shader which tested in games doesn't draw these sides, if seen behind the model (areas players aren't meant to access) the sides would be completely transparent where you could see in but players couldn't see out.
Yes level design is very close to set design in films, areas need planned based on;
-The size of the player in game
-Whats meant to happen in game
Its very hard to specify exactly what level design is, its very technical compared to the concept artist where the designers have to figure out where/how to place objects, to work out the lighting and general game physics, and to be able to do things which a game engine can understand. Its a way of working out how to do things which Iv experienced myself, for example;
In a previous level I worked on my task was to suggest to the player that a stone door doesnt work, the opening mechanism is operational but there is a mechanical problem i.e a large piece of debris on the other side which has crashed into the door and the door cannot open.
The way I did it quite simply was to have a trigger where I wanted the door switch to be once pressed (simultaneously)
>It would play a sound which I edited, in this case a Stone door attempting to open upwards, and then a piece of machinery giving way - out of sight
>It would activate a timer which at the precise moment in the sound effect where the machinery gives way a "Trigger_Breakable" would self destruct.
The result is an interpretation of a door refusing to open.
Where this is very long winded to explain its basically solving problems based around the limitations of a game engine. Its a large area where you could go on and on giving examples of how to suggest things in a game but its taking a concept, thinking about it and translating it through the senses.