The most basic harm of an addiction isn't financial. It's caused by an inability to be present in relationships with family & friends. A parent addicted to anything can't be bothered with anybody else's needs. They may hold down a job, and feed their kids 3 meals a day... But an addict won't be emotionally available to anyone around them. When they're actively getting their fix, they're numb to anything outside that experience. And when they're not, they're too busy struggling with their own unmanaged emotions to have room for their kids or spouse.
Video game addiction may not take all your money, but it can definitely devour the person. It'll leave you just as hollowed out and functionlly limited as a drinking problem. It's the core nature of self-medication, regardless of the mechanism of medication.