Games include two types of music:

Original music is created by the game creators and streaming rights are included in the software EULA.

Licensed music is created by third party artists and is usually not included in the software EULA because the music artist/publisher does not grant that type of license to the game creator/publisher. A gamer streaming gameplay that includes the copyrighted song will trigger automatic copyright protection on the streaming service they use and is subject to DMCA takedowns.

Modern games often include a "streamer mode" which replaces or mutes the licensed music.

Sure, but the claim being made was that this is a crime. In many places there are two types of law civil and criminal.

In the US copyright infringement is unlawful but it's almost always civil law.

The DMCA has both civil and criminal penalties. The criminal penalties include fines and jail time.

Yes, but again: why is this criminal and not civil infringement?

Can you point to the section of DMCA that you think turns this into a criminal offence rather than just civil infringement?