Well, for the first 5 years after publication, no. She would need to do nothing exactly as the world exists today. She would have an exclusive period of 5 years to monetize the book exclusively without having to register it, pay anyone, or talk to anyone.
After 5 years, she would have to pay $500 (again, exact value for discussion purposes, not a final proposal) and register it with a government website (with her contact information, and attesting that she still owns the work). After 10 years, she would have to pay again, and update the registration. Or, if the works are no longer valuable, she could simply not do that, and let the works enter the public domain.
The _entire point_ is that works that _aren't financially viable_ enter the public domain rapidly, and works that are continuing to produce financial value would be worth registration. >99% of works produced would likely never be registered (since every comment on a website counts as a separate "work"), and would enter the public domain after 5 years. Only a small fraction would be extended for 5 years.
But, yes, if you want exclusive rights to your game for 10 years, you'd have to pay a small amount of money and fill out a form on a website (my goal would be about the same difficulty as updating your whois information for a registered domain name). If it's not worth that amount of trouble, then the work enters the public domain.
> Everyone who makes a side project game on itch.io has to keep it online forever
My proposal had no _online_ requirement. So, no, that wouldn't be part of my proposal. Don't know where you got that requirement from.