I'm a senior software engineer, working on random web stuff forever, and I want to work in the games industry. I'm not in a rush, so anything I can do between now and the next two years I'll consider. I have some constraints though: I would like to stay remote, and have a "safe" job (I say that because I've heard many stories where people are hired to make a single game and are fired right after launch, which would be too risky for me).
Gaming has been my passion forever, and I even make some minigames in my free time. Right now I'm just trying to mix things up, to put my engineering skills into something I might like more. I understand that's a bit naive, but I have no reason not to try.
Skills wise, I would recommend spending a few years learning C++ at the least, try developing an engine from scratch, build an ECS, build some basic multiplayer implementations. I wouldn't expect much of your web experience to transfer, and you would most likely be joining the industry as junior.
Stability wise, if you have any backend experience, applying for infrastructure SWE roles that handle online services for video games is an alright bet, but that job market is quite small.