As with all other scientific things someone knows more than me, but I will give my opinion.
The last step is the greatest weakness. The result has to somehow be sent to the website and verified. If you have physical access to the device doing the verification then it will eventually be spoofed. A man in the middle attack would be easy enough given that the device absolutely has to go via a network the user controls.
Beyond the transmission issues, biologically there are not any markers that are a clear and simple age measure. Most biomarkers are more of a range with ages that correlate to some degree. You could say for example testosterone, but that goes up through puberty from a baseline in kids to an adult level, but the adult levels are really varied. Some people are higher than others and some XX people have higher testosterone levels than some XY people, and visa versa for oestrogen. So with the sex hormones out, you would want something that accumulates over time. Unfortunately that is going to vary by where a person lives and what they are exposed to. Honestly it is not at all workable.
That said, a simple solution which would make much more sense than any of this crap is to just have something on the internet account end. If the ISP can offer a check box for “Block adult sites and services” and people can opt in to that then kids will only get access to the full internet when their parents allow it or they are old enough to have their own device on their own internet plan.
If the government want to make a system to protect kids from adult stuff on the internet that is great. If they make it opt in that is all fine with me. But if they make it something you have to verify your age for, using things like state issued ID or facial inspection by an algorithm, then I think it is disastrous. It will be circumvented rapidly by people who are old enough to verify but simply do not want to. That technique will be shared with kids. Kids will be able to bypass it. This nanny state approach is not actually about protecting kids in my opinion. I think the companies involved will use the data, the face images for during verification, as training data for AI models, use the licence data for various profit driven business activities, and in the process make us all less secure. They will eventually have a leak or hack that exposes your data including what site you were on and your licence. The only question is when.
Just to clarify, it would be wise to avoid a lot of the language around scores and so on. Many of the mass shooters over the last few years have been related to the Terrorgram group, a bunch of idiots who glorify violence in the language of video games. They include the Christchurch shooter who live streamed his attack on a mosque in New Zealand. If you want to use the phrasing around a high score it would be a good idea to be very clear about what you mean as those idiots have a tendency to see anything that is not outright against them as probably in favour. If you are interested a podcast called Weird Little Guys is great for learning more about far right weirdos.