If you had a talk show called the [Your Name] show, should it be immune to bankruptcy courts? Should a the company [Your Name] Inc. not be allowed to be bought and sold? Should we forbid people from selling tshirts or pictures with their names and faces on them? Where do you think we should draw the line?
The same precedent applies to ordinary people too. Should a debt collector acquire your Facebook page? Because you used Facebook marketplace it’s now a business asset?
Most people don't own a business. The occasional use of facebook marketplace doesn't make a personal account part of a nonexistant business.
You're using the past tense, but they're very much still giving away games for free. On a related note for OP, I'm pretty sure amazon prime gives away games for free too, so if you don't know where to start, you can always start with something that doesn't cost you anything (extra, assuming you have prime).