According to Raffles on Head For Points, the Curve business model relies on the EU interchange cap being consumer-only, and not applying to Business Cards. That's why they need you to say you're a Business or Self Employer (or similar) customer, so they're allowed to then issue you a Business card. Apparently, those have interchange fees up around the 1.3% mark, far higher than the consumer 0.3% cap that's coming in, and provides their margin. So, Curve will net themselves around 1.3%, pay out only around 0.3% on the onward charge to your Visa / MasterCard (or higher but still sub-1.3% to Amex), and the rest is theirs to fund the whole thing
Cash Withdrawls they still look to loose money on, so I suspect they'll need to set the "fair use limit" on those pretty low to not loose out
Interesting thing for me will be what places will let you use it without fee. If it could be used with HMRC without their credit card surcharge, it could make a big difference. Utility Companies could be another good one - while I won't go to a huge amount of trouble to pre-pay my electricity for rewards on my points-earning visa card, for an Amex it's a different story. Some travel providers charge a fee for using a credit card, if any of those took it as a debit / no-fee card that'd help too.
We'll have to see what it's really like in a few weeks when they're sent out. Well, unless any of the private beta customers can shed some light sooner!