You do not pay additional VAT, you just pay the VAT of the country your customer is resident of instead of your own country. To do that you need to be registered in all EU countries and file VAT for each one of them.
There is an alternative for online services, etc called VAT MOSS[0], mainly meant for smaller sellers which allow you to keep paying VAT in your own country without registering in all of them but you still need to apply different VAT rates depending on your customer's country. Also you need to keep records of these transactions.
Steam (and other services... well actually even Steam uses an external service for this) handle that stuff for you and you only deal with Steam.
There is an alternative for online services, etc called VAT MOSS[0], mainly meant for smaller sellers which allow you to keep paying VAT in your own country without registering in all of them but you still need to apply different VAT rates depending on your customer's country. Also you need to keep records of these transactions.
Steam (and other services... well actually even Steam uses an external service for this) handle that stuff for you and you only deal with Steam.
[0] https://europa.eu/youreurope/business/taxation/vat/vat-digit...