I really wish the 13+ restriction didn't have to exist. However, I live in the US, and unfortunately the US has extremely strict regulations on this kind of thing.
In order to allow a child under 13 to legally make an account, WarLight would have to become certified by the government. I've heard this is an extremely difficult process, and can cost over $100,000 and has on-going regulations and complications. Unfortunately, it's really just not an option.
This is a very common problem for any websites made in the US. Even Google's GMail can't be legally used by minors. If you search, you'll find tons of stories of kids getting their GMail accounts permanently deleted just because they filled out a birthdate field. Example: https://productforums.google.com/forum/#!topic/gmail/V594OUj2pYM%5B1-25-false%5D
I can understand that the lawmakers feel like they're "protecting" the children, but the cost of getting a website certified for minors is so prohibitive that all they're doing is effectively cutting them off from the majority of the internet.
However, I believe it is okay for them to play single-player without making an account. Unfortunately that's the best that can be done.