I would go there
Chess-Themed Restaurant

Sounds fun for maybe a one-time visit, but sounds like this would get boring kind of quickly; the "rules" also sound harsh to get kicked out for breaking; maybe this would be fun if people tried to keep the restaurant "etiquette" (like walking as a Knight to food and Bishop back to table), but weren't kicked out if they forget it etc. (maybe a reminder from staff and only kicked out if intentionally neglecting these things often).

One word comes to mind. Bankruptcy.
Now if it were a great restaurant, and there was a chess theme, and you did away with all those requirements, then that's a different story. People go to restaurants for the food and to be waited on. A long list of requirements is a sure way to get rid of pesky customers. Plus the fact that very few people who eat are enthusiastic about chess or chess themed anything.
I’m guessing the restrooms will be called The en passant rooms?
Only if you cut the queue
You walk in and are immediately dressed as a queen or king. If you have kids they're dressed as pawns. These costumes will be ready for you at a moment's notice. The table is a big chess board and there are chess pieces to play with at your table that many other people have played with throughout the day. There's an open salad bar and the entire floor is a chess board. You have to move like a knight to get to the salad bar, and move like a bishop to get back to your table. If either of these rules are broken, you & your family are kicked out of the restaurant. In the restroom of the restaurant the toilets are rooks & you're peeing in the top of the rooks & that's where you sit. Every single item on the menu will be named after a chess opening, such as the Nimzo-Indian Omelet. You don't get to eat with utensils... Or, should I say instead, that the utensils you use will be Chess pieces.
When you're ready for the check at the end of the meal, you have to yell out "Check, mate!" To the waiter or waitress. If you don't yell this out then another meal will be added onto your bill for breaking the rules.
This is my dream for a restaurant.
I have put my life savings into this restaurant.
And now it's real, and it's mine.