After reaching out to the support, where they wanted me to pay for technician support time (so why do I pay for the PRO version?), I've decided to do that myself. So I came back here to write it for others who might want to update their nginx as well.
Actually, all I needed to do is edit /etc/yum.repos.d/nginx.repo and changing it to read like this:
[nginx]
name=nginx repo
baseurl=http://nginx.org/packages/centos/$releasever/$basearch/
gpgcheck=0
enabled=1
Note that the only change is changing "enabled=0" (in the original file) to "enabled=1".
Then run "yum update nginx".
You can tryp "nginx -v" to make sure the version was indeed updated.
Then restart nginx (can be done from CWP's dashboard) and you're done.