A Drupal module could be created that is able to access another website's database and display the data.
Drupal even provides a way to use its database abstraction layer. In the settings.php an additional $db_url has to be defined as described here: http://drupal.org/node/18429
There exists a Drupal-Module called Views. It is available for Drupal 5 through 7. It is able to output a site's data in XML (or RSS) format. That way a machine-readable format of the first site's data can be created.
For the other site a Drupal Module could be created that reads the XML file and formats it for output the way desired.