PixelBoy: Even if the price is WYSIWYG, the buyer must be told how much of the final sum is actual price and how much is taxes.
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In the end they add this: "All prices include VAT if applicable."
But nowhere do they say if VAT has been applied, and if so, how much.
Steam receipt is legal, GOG receipt... not so much.
That's not strictly true. I'm going to quote UK law here, but it will be the same in all EU states as VAT regulations haven't changed since Brexit and VAT rules are harmonised across the EU.
Firstly, GoG are only obliged to issue a VAT invoice if they are selling to another VAT registered entity (VAT Regulations 1995 (SI 1995/2518);
https://www.legislation.gov.uk/uksi/1995/2518/contents). So, if you contacted customer support with your VAT registration and asked for a full VAT invoice, then they would legally have to provide you with one. Of course, they would probably take the Epic Games route and apply the reverse charge (as it would become a B2B supply) and then pocket the VAT that they would have otherwise have paid on to the relevant tax authority.
The second get-out would be only if they have a rule that exists in the UK but may not exist in other EU states. This is for the simplified VAT invoice, which basically is for sales under £250. This version of the VAT invoice allows companies to omit the ex-VAT amount although would oblige the seller to include the VAT % charged.
In reality, they are likely relying on you not being VAT registered. Unless you're running a business that involves reviewing games (or buy gift codes for employees as gifts), it's unlikely that GoG would be making a VATable supply to a VAT registered entity.