Solution:
you probably want to use WordPress’s current_user_can() function to confirm the user has at least one capability normally associated with an Admin user, or is a member of the Administrator role.
According to that codex page, this should work to test for an administrator based on role, although I’m not in a position to confirm this sorry. I’ve certainly used this method in the past to verify user has a given capability.
<?php current_user_can( 'Administrator' ); ?>
EDIT: To authenticate users from a different site to WP, using WP credentials, this answer over on WordPress.stackexchange describes how to use WP’s built in XMLRPC service. The answer is written in the context of authenticating from a servlet, but cOnsumption of the WP XMLRPC service could be implemented in eg JavaScript at the client (rather than between your sites’ two separate backends) so might be more useful in your scenario.
The answer includes a pre-written plugin to handle the specific auth request from your remote client at the WP server… But note the comments below the question regarding use of a token instead of passing the creds over the wire (research “nonce” if you’re not already familiar with these… WP can created these for you).