My droplet IP is 188.226.235.21
Other sites hosted at this server are: cqlinc.com; tehnika.mk; petarpetkovski.com. They are working proplerly.

Here's the server block of the new website that is causing the problems. It is identical as the other sites except for the "server_name".

Tried reinstalling nginx, restarting nginx, but no luck.

server {

    server_name cqlcontracting.com www.cqlcontracting.com;

    root /var/www/cqlinc.com/html;
    index index.php;

    set $cache_uri $request_uri;

    # POST requests and urls with a query string should always go to PHP
    if ($request_method = POST) {
        set $cache_uri 'null cache';
    }   
    if ($query_string != "") {
        set $cache_uri 'null cache';
    }   

    # Don't cache uris containing the following segments
    if ($request_uri ~* "(/wp-admin/|/xmlrpc.php|/wp-(app|cron|login|register|mail).php|wp-.*.php|/feed/|index.php|wp-comments-popup.php|wp-links-opml.php|wp-locations.php|sitemap(_index)?.xml|[a-z0-9_-]+-sitemap([0-9]+)?.xml)") {
        set $cache_uri 'null cache';
    }   

    # Don't use the cache for logged in users or recent commenters
    if ($http_cookie ~* "comment_author|wordpress_[a-f0-9]+|wp-postpass|wordpress_logged_in") {
        set $cache_uri 'null cache';
    }

    # Use cached or actual file if they exists, otherwise pass request to WordPress
    location / {
        try_files /wp-content/cache/supercache/$http_host/$cache_uri/index.html $uri $uri/ /index.php ;
    }    

    location = /favicon.ico { log_not_found off; access_log off; }
    location = /robots.txt  { log_not_found off; access_log off; }

    location ~ .php$ {
        try_files $uri /index.php; 
        include fastcgi_params;
                fastcgi_pass unix:/var/run/php5-fpm.sock;
    }

    # Cache static files for as long as possible
    location ~* .(ogg|ogv|svg|svgz|eot|otf|woff|mp4|ttf|css|rss|atom|js|jpg|jpeg|gif|png|ico|zip|tgz|gz|rar|bz2|doc|xls|exe|ppt|tar|mid|midi|wav|bmp|rtf)$ {
        expires max; log_not_found off; access_log off;
    }
}

The new domain is loading your default website, have you removed this configuration?

When you installed WordPress on 188.226.235.21:81 the home and siteurl of WordPress were set to http://188.226.235.21:81

Now when pointing the domain name, WordPress is trying to redirect the domain to the IP:port URL.

Edit the wp-config.php file of this site and add the following code before /* That's all, stop editing! Happy blogging. */.

define( 'WP_SITEURL', 'http://cqlcontracting.com' );
define( 'WP_HOME', 'http://cqlcontracting.com' );