The problem is using the process of threatening legal action to suppress speech. This is the very problem that anti-SLAPP statutes are designed to protect against; if they're ineffective in this case, they should be amended to explicitly cover DMCA notices in a way that dissuades using them to suppress speech.

For what it's worth, using a brief clip of an emulated Switch game seems to me to clearly fall under Fair Use. It's transformative and does not substitute for the original work, often non-profit and/or educational, is a small portion of the copyrighted work, and fails to displace any sales.