In Chapter 4 of To Kill a Mockingbird, is their game an accurate depiction of the Radleys' house?

I do not think it is at all accurate. We can't know what really went on in the Radley house. The kids received their information about the Radleys from unreliable sources... people who would likely make up stories.

We tend to do this when dealing with the unknown. This unknown is certainly what stirs their curiosity, but that doesn't mean their game is at all true.

The Radley's keep to themselves in relation to the rest of the town. If one was to INFER what actually goes on in their house, I am sure they each have their own hobbies and individual activities that they do to keep themselves busy.

Led by their imaginative new neighbor, Dill, the Finch children spend much of their summer creating their own dramatic version of what they think goes on at the Radley Place. The kids play-act about Boo and his supposed exploits: Scout played Mrs. Radley, Dill was old Mr. Radley, and Jem took the part of Boo. The game progressed along with the summer, and the cast "polished and perfected it," adding changing plots and dialogue daily. Naturally, since the kids knew little about the mysterious Radleys, little of what went on had any accuracy. Boo probably didn't eat rats and squirrels nor bite off his mother's finger, and he likely did not "whittle away all the furniture in the house." When Atticus finally witnesses a bit of their play and catches them with scissors, he questions them if "this by any chance have anything to do with the Radleys?" Jem lies and tells him "No sir," but Scout realizes that the play's life is limited. Meanwhile, Scout thinks she hears laughter come from within the Radley Place: The children apparently have an unidentified but satisfied audience after all.

Is the game the children play in To Kill a Mockingbird an accurate depiction of the Radleys' home?

By Scout's own account, the Boo Radley game played by the children is really just "woven from bits and scraps of gossip" (To Kill a Mockingbird, Chapter 4).  Jem is the one who suggests they reenact scenes based on rumors they have heard about Boo and his family.  It becomes a favorite game of the children.  The three main characters are Mr. and Mrs. Radley and Boo.  At this point in the book, Scout, Jem, and Dill know very few solid facts about the Radley family.  They do not even know for certain if Boo is dead or alive.  Jem insists that he died years before.

As time goes on, the children further develop the storyline of their game.  They create a backstory for Mr. and Mrs. Radley:

Mrs. Radley had been beautiful until she married Mr. Radley and lost all her money.  She also lost most of her teeth, her hair, and her right forefinger (Dill’s contribution. Boo bit it off one night when he couldn’t find any cats and squirrels to eat.); she sat in the living room and cried most of the time, while Boo slowly whittled away all the furniture in the house (Chapter 4).

The highlight of their game is the most notorious rumor about Boo Radley.  It is a reenactment of Boo Radley stabbing his father in the leg with scissors.  This is a popular rumor told by Miss Stephanie.  To recreate this scene, the children take Calpurnia's sewing scissors.  Once they acquire the scissors, Jem, playing Boo, pretends to stab Dill, playing Mr. Radley, in the leg.  The game the children play is primarily based on rumors, so it is an inaccurate account of the Radley family history.