You know those Chinese restaurants where they perform tricks with fire and cooking utensiles as they cook in front of you. Is there a name for that style of restaurant?
Although the food served at them is anything but.
Yeah, I was surprised to find that out in the article. Still, I just felt like being snarky. 
Benihana
Yeah…I guess they are Japanese. I suppose I am confusing a Mongolian grill style of cooking (offered at some Chinese restaurants) with this style of cooking.
As the article states, Teppanyaki is considered Japanese and found in most Japanese restaurants in the US, but they are slim pickings here in Japan. Even if you do find one, usually it is because you are cooking your own food, such as in okonomiyaki (savory pancake/omelette thing) restaurants.
ETA: Most teppanyaki owners I have met (Okay, 2 out of the three that I’ve met) don’t even know how to cook Japanese cuisine. I can see the reasoning behind opening one though. Imagine you are a Chinese immigrant with a flair for cooking. You could start a Ming’s Great Wall or a Panda Express and sell your food at fast food prices or you could call it Japanese food, throw in some sushi on the menu, and serve it all for 25 dollars a plate. 
It is often referred to as “Hibachi-style” in the U.S.
Wikepedia entry on “Hibachi”. Scroll down to the last paragraph where it addresses your question.
There’s a couple around here which refer to themselves as Hibachi-style, as Tangent notes.
“Irritating.”
Teppan Grill.
Benihana
Benihana is the prototypical chain for this style but not the name of the style. If you were to look for one I would look for “Japanese steak house.”
A friend of mine was an Okonomiyaki chef. Jeebus but he provided such good food.
I’ve seen several Japanese that converted to this style. I guess it’s a better sell than authentic Japanese food. Plus people get a little suspicious if you have sushi and are a bit too far from the ocean.
Side note: if you ever want to piss off a hibachi chef (yes, I know, why would you, but bear with me), beat him to the “first week on the job” line. I’ve been to a lot of hibachi steak houses, and in my experience about two-thirds of the chefs will break that one out right before they try something dazzling, just to spook the newcomers.
Um, tourist trap?
You mean like this place?
Japanese hibachi-style grilling?
Venturing into MPSIMS territory here, I know, but…
Years ago when the ex and I lived in NoVa we went to a cut-rate stripmall version that had a bar in the front of the house. I ventured out for a drink and a smoke and a chat with a bunch of construction-worker types (imagine that, a road crew in a US 1 bar in NoVa) who told me it was their bar of choice as the “chefs” occasionally set things on fire. Like the ceiling lights.