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Depends on what you mean by "computer for gaming". You pretty much need a computer at home for school work, printing and sending documents, maybe even some work from home. A lot of this can be done with a phone or tablet nowadays, but that wasn't the case 5 years ago, which is why lots of people have an old-ish computer. And yes, this computer can be used to play games, not all the newer ones, but still plenty of games.

If you have a dedicated, modern and expensive computer only for games (and note that this includes consoles), yeah that definitely does exclude you from being poor.