Not at all. A bill of attainder is a retroactive statute, imposing criminal liability on an individual.
Here, the legal standard was added to the Constitution over 150 years ago. It does not impose criminal liability on anyone, or on anyone specifically. It sets one of the qualifications for being president.
The argument is that the Secretary of State of a state can make the initial determination whether a proposed candidate meets the constitutionally required qualifications. That determination would be subject to judicial review.