Hi Anama,
I can neither confirm nor deny that uChicago admits students without interview. It may be the case, but it seems unlikely. They told me in the interview that ~280 people applied this year to the program. I am unsure of how many interviews were sent out. Currently there are about ~168 graduate students in the department. My guess is that they enroll about 15-20 graduate applicants each year.
My interview at Berkeley was short and intense -> (Exactly 15 minutes), and was a panel interview with four interviewers.
My interview at uChicago was relaxed, gradual. In general it felt like they we're trying convince me to attend Chicago rather than see if I was qualified.
So I have no idea.
But be strong.
Sending you good vibes.