You are misunderstanding the word "replace" in that definition. Some viruses have RNA instead of DNA as their genome. The defintion does not mean that RNA can switch out your DNA.
RNA comes in many shapes and forms. mRNA is phsically incapable of altering DNA. There are other forms of RNA that influence the expression of genes - namely miRNA - but those are very different, uber small segments of RNA. The current vaccines only use mRNA since that is the RNA that is used to translate the spike antigen in the body.
Some RNA viruses are capable of altering human DNA, but those require very specialized biological machinery to do so. HIV for example is capable of inserting it's genetic material into human genomes, which is why HIV infections are life-long. However, this requires both reverse transcriptase and integrase enzymes, which the coronavirus does not have.
The complete ingredients for this vaccine are listed in the protocol at the end of this article. All drug developer are required by law to disclose their entire ingredients and processes in these protocols. These are lengthy and complicated to read, so I created this article to make it a bit more digestible, but all of the information is there for you to read.