i'm not sure on the specifics in other countries, but the USA has strict federal laws prohibiting interstate gambling activity. to avoid liability, banks and payment processors avoid transmitting money on behalf of sportsbooks and gambling sites. this naturally extends to exchanges, which is why coinbase and gemini have policies against usage for gambling in their user agreements. in fact, bitstamp does include something about "illegal gambling operations" in its terms. if the OP were from the USA or a country with similar laws, i wouldn't be surprised to see account termination over it.
and that's what would happen on coinbase or gemini---they would just close his account and send him his funds. leave it to bitstamp to put the OP through hell and possibly steal his coins because he can't prove the source of every satoshi.