According to a 1999 E.G.G. Complete Guide interview with the game's scenario writer/planner/supervisor Hiroaki Hara, he was asked what made him go for a fully illustrated 2D style for the maps. He responded:

"Hmmm… probably just our personal taste. Now that we’re firmly in the era of 3DCG, perhaps some of us may have wanted to go against that current. But in terms of what visual style would most fit the gameplay, for EGG we felt this was the best. This is a unique world that I don’t think can be rendered in polygons. Yet the Dreamcast is a polygon machine, isn’t it? We wanted to take advantage of that strength too, which is why the boss battles switch to 3D. The one thing we didn’t want, though, was for players to have to learn a whole new control scheme for the 3D fights, and we spent a lot of effort adjusting and revising it to feel right.

I would have personally loved to have more time to work on the game. But you know, we’d already spent 3 years… and if you consider the work we did before the initial pitch presentations, it’s even longer. I’ve never spent this much time on a game development before."
Contributed by ProtoSnake
In a 1999 interview in E.G.G.'s Complete Guide, according to the game's scenario writer, planner and supervisor Hiroaki Hara, and game designer (and designer of the titular E.G.G. mech) Hidetsugi Watanabe, they were asked when and why the mech was named the "Elemental Gimmick Gear"? Watanabe stated that he didn't give it any particular name, when he was working on the model. But Hara stated:

"That was something we started thinking about after the planning phase began. It looks like an egg—so the “EGG” was a simple association. Alone, the name “Egg” felt too simple and boring though. This unique powered suit runs from some mysterious combination of human energy and natural energy, so “Elemental Gimmick Gear”, abbreviated as E.G.G., seemed to fit perfectly."
Contributed by ProtoSnake