So 4chan that said they wouldn’t pay the UK fine as the UK doesn’t have jurisdiction over companies based in the USA is going to sue UK over stuff that 4chan can’t be responsible for?
4chan will sue the UK trying to hold them responsible for UK law, in US court. Foreign judgement limiting freedom of speech. Seems to be in line with their strategy of not being an UK company so not paying fines: “Your laws don’t apply to us. Hell, they aren’t even constitutional!”.
It’s more than that, I read the lawsuit. They argue that the whole network that we call the Internet was invented and is currently maintained by America (and they are not wrong), that other nations failed to invent and deploy competitive solutions and UK trying to enforce some rulings on an American network is absurd.

the Internet was invented and is currently maintained by America

why do I expect anything from 4chan?

Well, technically, if you look at

  • who manages and sells IP addresses allocations IANA
  • which organization controls domain name systems, top level domain naming and registrar assignments ICANN the USA has critical foothold in controlling the internet.

Hey, downvoteers, go read the first page of the lawsuit. Thank you.

Do you think the UK government even considered that? Do you think the Tories, who passed this law, or labour, who are full-throatedly supporting this law, even considered this?

They didn’t even consider vpns. We literally have a member of the House of lords talking about VPNs as if they were some obscure technology. She literally said “Have your heard of VPN”, one referring to it as if it was some sort of singular service.