It looks like Nginx is running on your droplet listening to port 80, so Apache can't use it while Nginx is using it.

Your website is loading fine so I'm assuming that you want to use Nginx not Apache. mod_rewrite is an Apache module, so if you want to set up 'clean URLs' in Prestashop, you will need to configure Nginx manually. Edit your server block config in /etc/nginx/sites-enabled and add the following block:

location / {
  index /index.php;

  rewrite ^/api/?(.*)$ /webservice/dispatcher.php?url=$1 last;
  rewrite ^/([0-9])(-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ /img/p/$1/$1$2.jpg last;
  rewrite ^/([0-9])([0-9])(-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ /img/p/$1/$2/$1$2$3.jpg last;
  rewrite ^/([0-9])([0-9])([0-9])(-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ /img/p/$1/$2/$3/$1$2$3$4.jpg last;
  rewrite ^/([0-9])([0-9])([0-9])([0-9])(-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ /img/p/$1/$2/$3/$4/$1$2$3$4$5.jpg last;
  rewrite ^/([0-9])([0-9])([0-9])([0-9])([0-9])(-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ /img/p/$1/$2/$3/$4/$5/$1$2$3$4$5$6.jpg last;
  rewrite ^/([0-9])([0-9])([0-9])([0-9])([0-9])([0-9])(-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ /img/p/$1/$2/$3/$4/$5/$6/$1$2$3$4$5$6$7.jpg last;
  rewrite ^/([0-9])([0-9])([0-9])([0-9])([0-9])([0-9])([0-9])(-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ /img/p/$1/$2/$3/$4/$5/$6/$7/$1$2$3$4$5$6$7$8.jpg last;
  rewrite ^/([0-9])([0-9])([0-9])([0-9])([0-9])([0-9])([0-9])([0-9])(-[_a-zA-Z0-9-]*)?(-[0-9]+)?/.+\.jpg$ /img/p/$1/$2/$3/$4/$5/$6/$7/$8/$1$2$3$4$5$6$7$8$9.jpg last;
  rewrite ^/c/([0-9]+)(-[_a-zA-Z0-9-]*)(-[0-9]+)?/.+\.jpg$ /img/c/$1$2.jpg last;
  rewrite ^/c/([a-zA-Z-]+)(-[0-9]+)?/.+\.jpg$ /img/c/$1.jpg last;
  rewrite ^/([0-9]+)(-[_a-zA-Z0-9-]*)(-[0-9]+)?/.+\.jpg$ /img/c/$1$2.jpg last;
  try_files $uri $uri/ /index.php?$args;
}

If you already have a location / {} block, you can delete it. Finally, restart Nginx so that the changes take effect:

sudo service nginx restart