返信遅くなりまして申し訳ございません。
助言ありがとうございます。

ec-cubeのルートディレクトリに移動して実行したら動きました。
インストールは完了っぽいのですが
EC-CUBEのindex.phpを見ると登録画面や商品一覧、お問い合わせなどにリンクできません。404エラーになります。

export ROOT_URLPATH=${ROOT_URLPATH:-"/"}

この部分のリンクかnginxの設定がおかしいのでしょうか？



eccube_install.sh内のConfiguration項目は以下のように設定してます。
# ---------------------------------------------------------------------
# Configuration
# ---------------------------------------------------------------------
export ADMIN_MAIL=${ADMIN_MAIL:-"admin@example.com";}
export SHOP_NAME=${SHOP_NAME:-"EC-CUBE SHOP"}

export ROOT_DIR=${BASE_DIR:-"/usr/share/nginx/html/***/html"}
export ROOT_URLPATH=${ROOT_URLPATH:-"./"}

export ADMIN_ROUTE=${ADMIN_ROUTE:-"kanri"}
export USER_DATA_ROUTE=${USER_DATA_ROUTE:-"user_data"}
export TEMPLATE_CODE=${TEMPLATE_CODE:-"default"}
export FORCE_SSL=${FORCE_SSL:-"0"}



------------------------------------------------------------
以下nginxの設定ファイル（default.conf）です。
server {
listen 80;
server_name localhost;
charset utf-8;
root /usr/share/nginx/html;
index index.php index.html index.htm;


#charset koi8-r;
#access_log /var/log/nginx/log/host.access.log main;

location / {
root /usr/share/nginx/html;
index index.html index.htm;
}

#error_page 404 /404.html;

# redirect server error pages to the static page /50x.html
#
error_page 500 502 503 504 /50x.html;
location = /50x.html {
root /usr/share/nginx/html;
}



location ~ \.php$ {
root /usr/share/nginx/html;
fastcgi_pass unix:/var/run/php-fpm/php-fpm.sock;
fastcgi_split_path_info ^(.+\.php)(/.+)$;
fastcgi_index index.php;

include fastcgi_params;
fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
fastcgi_param PATH_INFO $fastcgi_path_info;
fastcgi_param PATH_TRANSLATED $document_root$fastcgi_path_info;
}

error_page 404 /404.html;
location = /40x.html {
}


}



------------------------------------------------------------

以下実行分

update permissions...
creating /usr/share/nginx/html/***/app/config/eccube/config.yml
creating /usr/share/nginx/html/***/app/config/eccube/database.yml
creating /usr/share/nginx/html/***/app/config/eccube/mail.yml
creating /usr/share/nginx/html/***/app/config/eccube/path.yml
get composer...
All settings correct for using Composer
Downloading...

Composer (version 1.4.1) successfully installed to: /usr/share/nginx/html/***/composer.phar
Use it: php composer.phar

install composer...
You are using the deprecated option "dev". Dev packages are installed by default now.
Loading composer repositories with package information
Installing dependencies (including require-dev) from lock file
Nothing to install or update
Generating autoload files
dropdb...
createdb...
create table...
ATTENTION: This operation should not be executed in a production environment.

Creating database schema...
Database schema created successfully!
migration...

Doctrine Database Migrations


execute optional SQL...
cache:clear success
Finished Successful!