Surely the £12 admin fee is for the customs declaration and absolutely nothing to do with VAT.
When I worked importing aircraft parts we charged a flat £25 admin fee in every item. We also never took out insurance even if the customer paid for it, rather taking the chance it wouldn't get lost. A fairly substantial risk when some of the items were listed at over 250k.
As an aside the company (GlobalEyes) basically came about from working around duty clauses by arguing against HMRC that certain items for a bin wagon needed recategorising and were eligible for tariff duty payments.
I haven't looked at the specific ruling here, but expect that if a similar challenge was placed against the tariff that it could be argued that pinball machines do not fall under the tariff eligible for 25% duty.
The whole point of duty is to encourage companies to buy local, if you cannot buy that product locally the duty is usually 0%, or at least very low.
Duty is also lower for buying from third world countries to encourage trade with them.
(I will add that it's pushing 15 years since I worked in import/export, but the basic theory of duty won't have changed significantly in that time)
The way USA is handling Covid, it could end up as a third world country in the not too distant future anyway.