It looks like you took the screenshot while logged into your site. All I see is a logout link. Maybe you are not actually taking a screenshot and instead doing some type of screen recording that requires being logged into your site?
Most BPS Pro features work on nginx except for any features that do something with htaccess files. See this forum topic for more info > https://forum.ait-pro.com/forums/topic/bps-and-nginx/page/2/#post-40930.
You should be able to install and activate BPS Pro on nginx. So I assume the problem is due to some other problem on your host server. Did you install BPS Pro by installing the BPS Pro zip file using the WordPress Plugins Upload Zip installer?