If I compile my program and distrubute only the xychart4.ocx file to my customers, do I have to pay royalties?
No. Runtime distribution licenses are free. Specifically, if you only distribute the xychart4.ocx file and do not allow your customers to develop software using XY Chart, then there are no runtime royalties. If your customers can develop software using XY Chart, then this is effectively giving them a developer license. Therefore, in this case, a developer license must be purchased.