Wait, where are you seeing the link to HAI? TFA mentions something called "liftlab" which seems to be something under Stanford Law School and separate from HAI. The study has more than a dozen authors from as many different universities but HAI is not mentioned.
The leader of the study, Julian Nyarko, is Associate Director and Senior Fellow at HAI. I can't say whether that means the study was conducted by HAI, but there is at least a connection to it. https://hai.stanford.edu/people/julian-nyarko