It was originally owned by Lips Manlis, and it served as his base of operations. In addition to offering food, drink and entertainment (including the performers 88 Keyes and Breathless Mahoney), the Club Ritz also served as a covert gambling establishment which was able to quickly conceal the illegal activities when police arrived.
When Big Boy began his campaign to unify the city's criminal forces, his first act was to remove Lips Manlis as a competitor. Big Boy had several underlings kidnap Lips and Breathless from the Club Ritz while posing as police officers. Lips was forced at gunpoint to sign over control of his territory, including Club Ritz, to Big Boy. Big Boy then killed Lips.
Big Boy took over running the Club Ritz, continuing to use it as his base of operations. Dick Tracy planted Bug Bailey in the crawlspace above Big Boy's office, where Bug was able to radio information about Big Boy's plans to the police. Bug was eventually discovered by Big Boy and Pruneface.
The Blank kidnapped Tess Trueheart, hid her inside the Club Ritz, and made an anonymous call informing the police, intending to frame Big Boy for the crime. This resulted in a large-scale raid on the Club which took place on New Year's Eve. Big Boy found Tess and fled with her through a secret escape tunnel, hoping to evade capture.
In the follow-up novel "Dick Tracy Goes to War", Vitamin Flintheart had taken over a club that was previously operated by Big Boy, re-naming it The Stage Door Canteen. He employed several musical acts, including a "reformed" 88 Keyes, the mysterious singer Black Pearl, and the comical Spike Dyke and his Orchestra. There were still hidden rooms in the building, from which Mrs. Pruneface (who was employed as a cook at the club) operated her subversive organization. It is strongly implied that this is the Club Ritz, but that name is never explicitly stated.