In this comment there is a distinction drawn between "native macOS libraries" and X11,
Haven‘t used MacPorts for years, but most probably Kitty is compiled with the native macOS libraries, not with X11. So you need to either use an X11 version of kitty (if MacPorts has something like that), or compile it yourself with X11 support enabled. – nohillside♦ 7 hours ago
Is it possible to target either of those within MacPorts? Or is the port package defined for just one?