Nginx rewrite URL only if file exists

You don't need the error_page directive here, since you already have @thengine as the last part in your try_files directive. To answer the actual question, I need clarification what you actually want to happen..

For your actual use case, I think this is the most simple solution. You could modify the @thengine like this:

 location @thengine {
     rewrite ^/(.*)\.(htm|html)$ /$1.th.html;

     if (-f $request_filename) {
             proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
             proxy_set_header Host $http_host;
             proxy_intercept_errors on;
             proxy_redirect off;

             proxy_pass http://thengine_backend;
             break;
     }
     return 404;
}

However, I am not 100% sure that this configuration is safe, because of this article: https://www.nginx.com/resources/wiki/start/topics/depth/ifisevil/.

The current implementation of the if directive in nginx easily causes unwanted side-effects, and the implementation needs to be properly checked. After reading the article above, and the article explaining if behavior, I still am not sure whether this solution is safe.

A safer solution could be implemented with a Lua script.

As you didn't define a root path for image location nginx uses the default one - /usr/share/nginx/html/. If you want these files to be fetched with proxy_pass you need to copy the configuration for proxy_pass to this location too.