I just tested again with exact same render settings as in your screenshot and my rendered file is 1080×1080.
But how do you check your video still is 1920×1080? Did you already try to analyze via MediaInfo?
My guess is your result may also be 1080×1080 but with black bars on bottom and top because (of course) the video is neither stretched nor cropped to make the 16:9 format fit the 1:1 frame now.
If that it is you need to further edit your timeline events, while cropping is the prefered method.