As I recall, neither of you are technically correct. While I do not have access to the game at the moment, both my memory of the particular level, as well as every gameplay video I can find, all suggest that the game renders the exterior of the Dyson sphere as a flat plane extending in all directions, with the exception of the aperture that leads to the interior. This makes sense from the perspective of game/program development, as it's much easier to simply repeat a tile 'infinitely' than to generate an immense object larger than most computers could probably render back in 2003. Simply having it extend off to the edge of the map is not an issue, since all the creators needed to do was imply its enormity. Plus, the story directs the player to simply enter the sphere with a sense of urgency, which precludes too much exploration, and the level is not otherwise accessible (without mods).
I believe, however, that your perspective is the most correct. Once inside the megastructure, it clearly is meant to appear spherical, and is referred to as a Dyson sphere by characters in the game. There is no reason to believe that it is a cube at all. Your suggestion that it appears flat because of the imperceptible curvature of something that large is likely the impression the designers were hoping for.
