My question is, why on earth would you choose to be an impoverished freelance writer if you have a law degree? It's not steady, reliable income, especially when you're trying to start.
There would definitely be demand for people who can convert legalese into well-written English. There are numerous legal publications and trade magazines you can contact. Many law firms and law schools would likely want communications people. All those potential clients would demand someone with a firm understanding of the law, and capable of lawyer-like precision in their writing. Those aren't things most freelance writers could offer, but you could.
That kind of work would be more lucrative and less competitive to start with, and you can use that as a base to branch out into areas you may have more interest in. Everyone want to write the fun stuff, but if there's more money to be made leveraging your expertise to write for better-paying clients.
For example, I have a friend who was for many years an editor for newspapers, and for general interest and business magazines. He quit his job as editor-in-chief of a business magazine to work as a freelance writer/editor/communications strategist, mostly with corporate clients. He spends little time writing interesting magazine stories now, because those corporate clients provide steadier, better-paying work. I don't know what he's making, but I imagine it would have to be comfortable middle-class income or else he wouldn't have left his magazine position.
I only occasionally take corporate clients, and they don't bat an eye when I charge them more than double what magazines pay. And they cover all my travel expenses when I'm on assignment — flights, hotels, rental cars and meals — whereas magazines are much stingier.
So start in the legal world and branch out from there.
If you want to get into gaming journalism, or any kind of journalism for that matter, it's important to learn the rules and conventions of journalism writing. Journalism writing is its own genre, with many sub-genres within it. For example, I'm a food and travel magazine writer, but I also have experience in hard news journalism for newspapers and newswires. A 500-word hard news story has a very different structure and style than a 3,000-word magazine feature.
If you don't know those rules and structures, your portfolio pieces will immediately stand out to magazine and website editors as unprofessional.
So I'd strongly suggest taking some courses in whatever field of writing you'd like to get into. Journalism school is the conventional approach, but it's longer and more expensive than some other options.
I took a 6-week, non-credit magazine feature-writing course many years ago, and it taught me more about feature writing than anything I got when I went to journalism school later on.
Nowadays, there are several online courses and programs, such as this one: https://www.coursera.org/specializations/become-a-journalist
You can pick out one or a few courses you feel will suit your needs.
That said, it sounds like you're on the right track, and with your education you've got a great base to build upon.
Yes, avoid the content mills. Aim for well-paying clients to start with, and don't lower your standards. People who pay writers shitty rates are usually people who don't care about quality, so you won't get to work with good editors. You won't build a quality portfolio that way, and you won't get good feedback to help you improve your skills.