The wheels were already in motion for Tony to have Richie killed. He told Sil in the back of the Bing that Richie "wants to have me popped" after the meeting with Junior at the doctor's office. He was a goner. Silvio was on it. Richie just happened to get killed by Janice that night.
In the scene that night when Chris and Furio are cutting up Richie at Satriale's you can clearly see the blade isn't moving in the saw. Also, when Richie is about to get shot by Janice and he's leaning back in his chair, you can see someone's hand from under the table holding the leg of the chair to keep it steady. I never noticed either on first watch, but I can't not notice either now. Ha.