I'm unsure if they like ginger or not - I've seen kitties eat some pretty strange things, and it's probably an individual preference.
I am unable to locate any source that says Ginger is toxic to cats or should be avoided by cats. Therefore, I would say you can give your kitty a tiny bit of ginger cake as a treat (remember to only give a little bit - think about cat treats in general and how small those are). Too much may cause an upset tummy, so just give her a little bit.
Please let me know if I can assist further.