Copyright Disclaimer under section 107 of the Copyright Act 1976, allowance is made for “fair use” for purposes such as criticism, comment, news reporting, teaching, scholarship, education and research.
Fair use is a use permitted by copyright statute that might otherwise be infringing.
Non-profit, educational or personal use tips the balance in favor of fair use.
As a parody, this use of copyrighted footage of the debate is protected by fair use. It is a transformative use, non-commercial, and will not have a major effect on the value of the footage. The use of a small portion of the soundtrack from "Gladiator" is de minimus in terms of length, on top of being protected for its non-commercial, transformative, and financially inconsequential use. The brief clip from the Matrix is extremely brief and similarly protected by the other factors of fair use.
It is a violation of federal law (DMCA) to misrepresent legal fair use content as illegal. While Google (Youtube being its subsidiary) is free to bring content down on any grounds it pleases, it is not legal for a copy-right holder (or parties acting on their behalf) to misrepresent fair-use content as infringing upon copyright, as a DMCA takedown is essentially a threat to sue Youtube (Google by extension) if they do not comply with the DMCA.