Citing papers, that are cited within a paper?

This will all become much clearer if you shift your perspective away from paraphrasing and towards giving a context for your own work. Start by pretending that the other paper doesn't exist, and asking: "What does the reader of my work need to know about this concept?"

When you know that, and you know what level of detail you want to go into, then you can look to the other paper (and other things as well, I hope!) as a source of information to help you build your discussion of the context of your work.

A useful phrase at this point is: "A thorough discussion of [subject] can be found in [review paper]." Then you can explain your view of the material, which the reader will understand is heavily influenced by the nice review paper you've just cited. In digesting the review to produce your own explanation, you will need to choose what you think are the important points for understanding the context of your work, and the key references supporting those points will be the ones that you should cite: as these references are the ones that were important for your understanding, so too should they be for your readers.

The suggestions by earthling and jakebeal are sound advice. I want to add, risking to provide an answer that actually is not answering the question that there is a caveat to citing material without checking the sources. When you do not check the original source you run the risk of propagating errors. You do not know if the way in which a particular source is correctly made and you may find that your take home from a paper is not the same as the source from where you were thinking of citing it. You should therefore, as much as possible, avoid to cite sources that involve also taking other author's interpretation of the original results or conclusions.

This may see like a minor point but errors that are propagated this way can become very destructive. In some cases errors like this may become"truths" that are very hard to correct. So while you can cite a source by as ref1 cited in ref2 you should make every effort to avoid it.

While jakebeal's answer is a fine answer, I wanted to add that there is actual accepted format in some referencing system. For example, in Harvard Reverencing, your paper would contain (here is where you would actually shorten it down as you desire):

Stanley and Miikkulainen (2002, cited in Smith, 2014) argued that the topology of a neural network also affects their functionality

This way you are saying that you did not read the paper by Stanley and Miikkulainen but you are giving the original authors credit, while still providing a source for your understanding, which the reader might want to check.