This affects all sellers regardless of where you are located. In 2015 the EU launched a initiative to force all online sellers to collect tax from European buyers. It is called VAT MOSS. To be VAT MOSS compliant you must select a EU country to register with (ideally one where you can speak the language, or they have English available. Ireland is a good option with the UK leaving the EU), and then every quarter you report how much you have collected from each country and wire them that amount.
On your itch.io dashboard you can download CSV reports of purchases that you can use to generate the amounts that you owe. Since we also process VAT on purchases that we manage, we automatically keep track of VAT rates, take care of identifying where a buyer is, and add the appropriate amount on top of their purchase, unless you explicitly disable that from happening.