My mom has kinda always been like that. Old, old fashioned, perhaps even very overbearing. She just has a lot of expectations for me, and I have to be responsible for the other two family members when she's out of the house.
Wish there was something I could do...
Just read all your posts about it in the social thread. Since it looks like the topic moved away from there, I will respond here. Anyways, I can relate to your situation to a degree. The difference is I don't have to take care of a sick parent or relative, and my parents never banned video games because they don't see me playing video games that often. Also, since I paid with my own money, they can't really do anything about it. Also, I'll be turning 24 in less than two weeks instead of being 25.
What I did earlier last year was to apply for part-time jobs as well until I could get a good job. I got a part-time job doing retail. While it's better than not having any sort of income, I still am trying to find a good job and still having to deal with the pressures of parents pressuring me to get a better job. I applied for navy officer training which I won't hear back from until spring, and that's not even guaranteed I'll get in. I've also been asked to apply to grad school, I suggested applying for a 3 month computer science bootcamp would be much better than going back to take a new undergrad degree, and now I'm trying to learn some coding on my own before I can apply for that. Preferably, I would find a job before I can do any of that, but so far, I have been unsuccessful.
Anyways, I know it would be hard to move out. You don't have a job, and you have sick family to take care of. I've had many people tell me I should move out because they think the environment I'm living in is toxic to me, but I can't really move out if I'm not making that much money to support myself. If I were able to get a good job, that could actually be an option. However, there are questions I have. What happens if you eventually can get a job, and it happens to require you to move? Or what happens if you end up marrying someone? Would you still be living at home under those kinds of situations? And before the meaning of one of my questions gets twisted because Internet, I am not saying I want to marry you or any other stranger online.
If you paid for all your games on your own, I can definitely see them being taken away as unreasonable. However, if it was from money earned by parents, I can see why they think they have the right to take it away. They want you to be successful, but they believe games are getting in the way of that. I know you got let go from one job because you had trouble appearing to be sociable, but I would like to suggest that you keep applying to other jobs like part-time jobs. If you can at least get that, you will get experience interacting with customers or other kinds of work experience, and it will somewhat help with your resume as you apply for other full-time jobs. I would say to move out, but considering I'm in a similar situation, it would be hypocritical. Also, I understand it would be difficult considering you don't seem to have a source of income and you have sick family to take care of. Good luck with everything, and I hope your situation can improve.