patrikc: I can't tell since I have never asked for a refund, but I believe it should be stated clearly in the email, it would be odd otherwise.
Here's an excerpt from GOG:
Cash refunds can take a few business days, depending on the exact payment method used, your bank, etc. There are some exceptions, such as paysafecard, SOFORT, and GiroPay - for technical reasons, these transactions need to be fully processed before they can be refunded; this can take up to a few weeks. My guess would be a few business days, 2-4 most likely. At least that's the normal around here.
As that message notes, it would depend on the method you used for payment and how long ago you made the purchase.
If you used a method (e.g. a paper check) that takes a while for the actual underlying $$ payment to come through, any smart vendor is going to sit on a refund until they receive the actual $$ behind the payment - if they don't do that they've got an open invitation for transaction fraud because the initial transaction by itself is more a promise of money than actual money.
That's the mechanism a lot of internet scams use: "Please deposit my $5,000 transaction that takes weeks to validate and I just need you to send me a small chunk of that back in a way that's validated before you figure out you've been scammed!""
If you used a credit card, that is comparatively quick and straight forward.