It does not change the meaning. The most formal and grammatically correct phrase would be "it has all of the amenities." In colloquial English we can leave out the word "of" and say "all the amenities." We can go further and leave out "the" and say "all amenities." None of these have any precise meaning. There is no official list of what "amenities" a kitchen. It is just saying in a vague way that it is a complete kitchen that has the things you'd expect to have in a kitchen.
"All the amenities" is vague. The writer is trying to make the kitchen sound good, in order to make up for there not being a living room. "Cosy" means that the kitchen is small! Again, the writer is trying to make the kitchen sound good. The IMPRESSION it gives it is a real kitchen, with stove, oven, refrigerator, microwave, sink--not just a hotplate, say. However, if it is important to you to know the details of what is in the kitchen, you would have to ask. For example: how many people does the table seat? Does it have have a coffeemaker? Are pots, pans, and silverware provided?
Particularly in short descriptions of this kind, people start to use "telegraphic" English. To be short, people start to leave out any word that isn't necessary. "Telegraphic" English isn't grammatically correct. If the person were writing an ad and was paying by the word, they might have said "Cosy kitchen w. dining table, all amenities. Bike storage."