Is it possible to run 2 different sites in Acquia Dev Desktop on the same computer?
Yes, you can install more than one Drupal site on the same computer using Acquia Dev Desktop. Check out Acquia's documentation here:

https://docs.acquia.com/dev-desktop/sites/

It looks to me like maybe you have specified an identical name for the local database. The error screen that you see is one that commonly appears when a new Drupal installation attempts to run install.php but the database is already set up.

As an experiment, click on the link that says "View your existing site." If my hunch is correct, you should see the content of your other site.

Instead, try selecting "Create a new database" when setting up the second site, and make certain that you give it a different name than the first site uses.

If the two cloned sites just happen to have identically-named databases, you should still be able to create a new one with a new name, and then import a sqldump of the second site's database into that.