Hi Fluxus and welcome to the Forum.
Please note that both website and Quick Guide state that the minimum requirement is macOS 10.11. AmiKit X was tested and proved to work on 10.12 and 10.11. But don't worry, it should work on 10.8+ which is the minimum requirements for wine. It was just not tested on macOS below 10.11.
Anyway, the Screen Mode requester should display at least some screen modes for you. It should not be empty.
First of all, please update wine to see if it has any impact on this screenmode requester. Find the instructions in AmiKit Quick Guide, page: 12.