Biscuits (cookies) turning out more cake-like than biscuity
The recipe calls for self-raising flour, which has a raising agent in it which causes the dough to rise in the oven. Risen bakes will be soft, so you'd be better off using plain flour. I'm surprised a recipe for this type of cookie would call for self-raising flour. Most recipes call for the butter and sugar to be creamed, that's simply beating the butter and sugar together until it's light and creamy. I'm not sure if you'd get the same result with xylitol, however you could still cream the butter to get it light and fluffy.