It’s a non for profit organization.
It’s not a business or a public company so .com doesn’t apply, it’s not an ISP or a company that provides networking services so .net doesn’t apply.
It’s not a military organization, educational institution or a government agency so .mil, .edu and .gov are not applicable.
Like it or not political parties was exactly the intended target for a .org domain registration.
It is absolutely a for-profit.
They have no party members, other than the three members of the Ltd co - their supporters are merely subscribers. They have no voting power, unlike in political parties.
Here’s their entry in companies house, which makes this explicit - you’ll find no such entry for, say, the Conservative and Unionist Party, or the Labour Party, or the Liberal Democrats, as they are political parties, not companies.
https://beta.companieshouse.gov.uk/company/11694875/officers
So, no, they shouldn’t be a .org, it’s misleading, just as it has evidently mislead you.
Frankly, I find it extremely worrying that a private company stands to potentially govern. Will their accountability lie with the public, or their shareholders?