cjrgreen: GOG doesn't worry about it, so long as your money is green enough...
AstralWanderer: That's not quite true - you may find your credit card being (falsely) reported as invalid. I've used
Tor for all web access for the last 5-6 years and did fairly recently encounter this. I did "solve" this by contacting customer support who then relaxed the IP address settings on my account.
There is a risk in using Tor, since the exit node can monitor your traffic (though they'll only typically see 10 minutes' worth and, without identifiable data in the network data can't tell where it came from) but that's far smaller than the risk of ISP/government monitoring in my view. HTTPS traffic won't be subject to such monitoring (so purchases can be done safely, though some merchants may give you trouble - Paypal will throw a fit immediately and block your account) but do be aware of how HTTPS exploits (like
SSL Strip) work. Double-check that financially sensitive pages *are* using HTTPS and if your browser reports a certificate issue, change exit node.
That's not GOG's problem; it's the card issuer's.
If the card issuer won't honor a charge from a company in Cyprus, GOG can't collect and has to block the sale.
Many US card issuers, especially Visa franchisees and prepaid card operations, block "card not present" charges from many countries. This is entirely legal, entirely within their scope of doing business as they deem prudent, and damn frustrating if you the consumer, or GOG the merchant, can't make a deal because the charge was declined.
Nothing you or GOG can do about it except refuse to deal with those companies.
The problem with TOR is that it is used for so much really heinous stuff that any law enforcement that traces TOR traffic to you is going to put you on a list of probable child pornographers. Since the TOR endpoints are largely known to law enforcement, it becomes child's play to determine that you are using TOR, even if they can't discern the content.