Federal Laws Protect Zoo Animals, Not Visitors
Enacted to enforce the federal Animal Welfare Act, regulations adopted in 1994 require only that outdoor exhibit facilities housing wild animals be enclosed by a fence of "sufficient height" to keep "unwanted species" -- including humans -- out.
"Fixed public exhibits housing nonhuman primates, such as zoos, must have a barrier between the primary enclosure and the public at any time the public is present, in order to restrict physical contact between the public and the nonhuman primates." (Title 9, Sec. 3.78 -- Code of Federal Regulations)
The U.S. Department of Agriculture's Animal and Plant Health Inspection Service enforces the Animal Protection Act to ensure the safety of wild animals confined in zoos, circuses and marine mammal parks. The USDA regulates the care of all animals exhibited to the public or used in research or teaching.
According to an AP report, a USDA inspector will determine if the tiger enclosure at the San Francisco Zoo was sufficient to prevent tiger-human interaction.
Under the USDA's realm of authority, if an insufficient enclosure contributed to the tiger's ability to interact with humans, which ultimately resulted in the death of the tiger, further enforcement action could be warranted.
Also See:
Federal Regulations: Laws Behind the Acts
Federal Laws and Regulations: A Primer


Comments
As I understand it, the law that you quoted relates to primates, not to felines. Is there a similar law that concerns big cats?