The DNS provider (who is not necessarily also a registrar, but it's common that the registrar is also a provider) doesn't have any option to disable individual pages. They can only disable a whole subdomain or domain.

The server provider technically could, but it's much harder because the site is served on https, so they would most likely have to disable the whole server as well.

Not that the server provider was asked, it's just to illustrate that no one but the service owner (itch.io) can meaningfully block a single page. Asking the infrastructure providers is a dick move.

Edit: So the server provider was asked as well, but they're not as incompetent it seems. Also, instead of a copyright abuse, BrandShield falsely sent this as a fraud and phishing, which is another dick move.

So yeah, the DNS provider is incompetent, but BrandShield is the malicious actor here.