I think you may be overreaching to assume you're "just as qualified" as the other person who got an interview. It's always upsetting to be passed over for an interview, especially when other people get an interview who didn't formally apply, but presumably these people probably have some advantage that you don't. Maybe they had a stronger SoP, or they had a better fit with the program. I'm not saying this to be mean, but just to caution you against "raising a stink" which may burn bridges for you in the future. Offering interviews to students who fit better with another program is fairly common practice for a lot of schools.
I did the online interview last Thursday, haven't heard back yet about on-campus interview. When I sent a thank you email afterwards, the admissions director told me they'd get back within 1 - 2 weeks. So could be anytime between today and the end of next week.