I don't think there are any restrictions in the tax-free system on which kind of items it can be applied to, but as you can read on the page you are linking to in the question, it only applies to goods you are bringing out of the Faroe Islands. If you buy anything valued 300 DKK or above from a retailer participating in the tax-free scheme, you will first have to pay the regular price (incl. VAT) to the retailer, but you will get a tax-free cheque with details about your purchase. When leaving the Faroe Islands, you have to present the goods to a customs office, get a confirmation on the tax-free cheque that you have left the island with the goods and then you can cash it in at a tax-free agent and get back the VAT you previously paid.
It can therefore not be applied to meals or drinks, which you buy for immediate consumption, but you could use the tax-free system and get a VAT refund if you want to bring Faeroese food or beverages back home.