To stray back into 'some online commentator' though, I believe that may be outdated: I think it's now wholly Waitrose, just a brand. (Notice there's no Essentials/Cooks Ingredients organic brand/products - if it's organic it's Duchy Organic.)
(At least if you believe the figures from Visit Britain, the government organization for tourism.)
That said, it seems silly to argue it brings no tourism whatsoever, and indeed the page you linked doesn't - it claims £500M, which it (fairly enough) goes on to say is negligible in the scheme of UK total tourism revenue and economy.
But that's not the point is it - when people make the claim it says is wrong, or certainly for the point I was making (again which I think tourism can be ignored for anyway) it's about expense vs. revenue from the royal family, i.e. whether there's net income - because if there is then it seems a futile argument for republicans to say they 'cost too much' - not whether or not that income is large enough to put a meaningful dent in GDP.
I don't much care about the costs, but it is a good demonstration of how opaque this part of government is.
(Because we pay taxes to the crown, doesn't really make sense for the king to pay tax to his majesty's own revenue and customs, HMRC. That said, there was something in the accension council about continuing to volunteer tax on something or another, and as the Duke of Cornwall he volunteered tax on duchy income. My understanding is that the royal family is a net contributor to state coffers even without (how would you even begin) accounting for all the tourism income.)