A group of individuals are sitting together in a room.
The people are celebrating their father's birthday at a local restaurant.
You can not infer they are celebrating a birthday.
No acts related to celebrating, such as toasting or embracing, are mentioned.  Nothing indicative of birthday parties, such as balloons, cake, or other decorations, are in the original sentence.  There is nothing to show that it is occurring in a local restaurant, just in a room without mention of waiters or other items typically found in restaurants.  It being a gathering of relatives, especially of a father's party, is indiscernible from the statement "a group of individuals."
Sitting together in a room does not mean at a local restaurant.