i have not been to teppan edo in japan personally so what i am about to say it my guess - not actual fact.
as a vegetarian, i would not expect to be able to eat there because the food is generally all cooked together on the same grill, with the same utensils, etc. as all of the meat products.
now - i'm not stupid enough to believe that doesn't happen in the kitchen - but at least then i can convince myself it is cooked separately - out of sight, out of mind. (some restaurants do actually cook veggie items separately.) at a japanese restaurant like that it's right in your face and not terribly pleasant.
not all vegetarians feel the same way that i do - some will gladly pick the meat out of their meal, etc. i'm just not that accepting. ask them how they feel about it and take it from there.