It's a much higher risk than average because games are often abandoned within one year of release and still run as long as 10-15 years later and connects to the internet and other randos on the internet. See the Call of Duty games that allow you to take over the computer of anyone who connects to your online match. It greatly degrades the security of its users.

Technically lots of things people call "malware" don't actually do any of those things. For instance they may hijack your default search engine, pop up ads, or otherwise monetize your computer at your expense. The category that was invented by ass coverers is "possibly unwanted program" but outside of those who worry about being sued by scumbags people colloquially refer to both what you call malware AND PUPs as "malware the root of which is "bad" after all. Language being descriptive not prescriptive I think this broader definition of malware is fine.