Is Mac OS X Server 10.6 upgradeable to latest Desktop OS X (without Sever.app) Around 2010, my boss purchased a Mac mini Server with 10.6. (Macmini3, 2.53 GHz Core 2 Duo, 4 GB RAM)

This server was retired last week.

Is the Server License (unlimited client) eligible to upgrade to a new release of OS X (Mavericks or Yosemite) or do I have to buy a new license?
Once all the updates have been installed and OS X 10.6.8 is installed the App Store suggest to upgrade to OS X 10.11.6.

Therefore, it plays no role whether it is an OS X servers or a "normal" OS X.
As soon as it is 10.6.8, it is eligible to upgrade.