For the marketing dynamite of being the only $8.03 "at-cost" registrar, they are going to take a payment processing hit of around ten to fifteen cents per domain. They could shift that cost to the price, but then they would lose those invaluable bragging rights.
The point is not that customers save a few cents, but the absolute transparency of paying exactly the registry cost + the ICANN tax. The simple math of $7.85 + 18 cents implicitly suggests that you are dealing with an utterly fair company: not a penny more, not a penny less. $8.03 will gain the attention of the big companies they want to attract in a way that $8.13, $8.18 or $8.20 never could. In this context, $8.03 is actually a far more powerful price than $8.
There are plenty of other costs associated with running a registrar, not just payment processing fees, but the whole thing is intended as a loss-leader to attract new users and coax their existing, non-paying users into a paying relationship. From there, with a credit card on file, it becomes far easier to sell them higher-margin services.
It will also deepen their relationship with their existing paying users, making it a lot harder for competitors (present or future) to lure them away.
When you consider the cost of customer acquisition through normal marketing channels, positioning themselves as the only "at-cost" registrar is a stroke of genius. Reminiscent of Apple disrupting the phone business, Cloudflare have chosen to disrupt a particularly messy, flaky industry that no customer loves. If they manage to pull this off at the $8.03 price, it will catapult Cloudflare to a whole new level.