Eh? If you follow the actual initial rules of tLDS then it should be a .org.

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.

Eh? The Brexit Party Ltd is a limited company, not a political party. They are acting like a political party, but they are a limited company, regardless. See, for instance, the fact that Farage is their immutable leader - he himself has explicitly stated that there will be no leadership contests within the party, as it is not a party, and he is the Person with Significant Control, with a 60% shareholding, with four anonymous individuals or organisations holding the remaining 40%.

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?

They bought this domain to prove a point which they thought it might be amusing to a certain type if audience. Don't read too much into it.