I ran into this exact problem, which had me stumped for a while. The problem is that Nginx needs to execute as root and let the user directive in the /etc/Nginx/Nginx.conf handle running everything as the correct user. For me, I had the system job defining the user to run Nginx as. Try setting the permissions for /var/log/Nginx/ to 766.
sudo chmod -R 766 /var/log/Nginx/
I guess this will help.
Thanks