Readers are not actually told the cause of death for Mr. Pignati. We aren't even given a decent description of his final moments in order to check for signs and symptoms of a cause of death. We know from the end of chapter 10 that Mr. Pignati had an earlier heart attack.
He started to double over—his eyes fastened on me—gaping like
a fish out of water. Then he pressed his right hand to his chest and
fell to the bottom of the stairs.
Chapter 11 confirms to readers that Mr. Pignati suffered a heart attack, but he survived this particular episode. Chapter 13 has John and Lorraine having the party at Mr. Pignati's house, and the chapter ends with Mr. Pignati coming home. That's when John passes out. Mr. Pignati does not have a heart attack or pass out at this moment like a previous answer shows. In chapter 14, Mr. Pignati, Lorraine, and John are back at the zoo. Near the end of the chapter, the three characters are at their favorite baboon exhibit, but Bobo is nowhere to be found. It turns out that Bobo died the week before. The news is devastating to Mr. Pignati. His hands begin to shake, and he lets out a "tiny cry." He then drops to ground, dead.