In this case, your quote is only one third of the content. You are not quoting the first sentence or the last part, which is why the quote doesn't make sense.
Your quote should read the following, where I've italicized the two parts you left out, "NO EFFECT ON CHILD SEXUAL EXPLOITATION LAW.—Nothing in this section (other than subsection (c)(2)(A)) shall be construed to impair or limit— any charge in a criminal prosecution brought against a provider of an interactive computer service under State law regarding the advertisement, promotion, presentation, distribution, or solicitation of child sexual abuse material, as defined in section 2256(8) of title 18, United States Code;"
Your quote should read the following, where I've italicized the two parts you left out, "NO EFFECT ON CHILD SEXUAL EXPLOITATION LAW.—Nothing in this section (other than subsection (c)(2)(A)) shall be construed to impair or limit— any charge in a criminal prosecution brought against a provider of an interactive computer service under State law regarding the advertisement, promotion, presentation, distribution, or solicitation of child sexual abuse material, as defined in section 2256(8) of title 18, United States Code;"