I would like to use part of the XMLSpy® 2015 COM API functionality in one of my applications. Do I have to buy a license of XMLSpy® 2015 for each user who will be using my application?

Yes it is necessary to install XMLSpy® 2015 on each machine on which your application will be installed as well as purchasing a license of XMLSpy® 2015 for each user who will be using your application.