This is an interesting concept - essentially the loyalty coins would be mined by the company providing them and consumers could use them for purchases. There would be the benefit that the coins could only be spent at participating retailers as opposed to giving out bitcoin that could be used anywhere, however I'm note sure that there would be sufficient benefit of using a bitcoin style protocol as opposed to the current systems they are working on - the individual user of loyalty programs has no vested interest in confirming that all prior loyalty purchase transactions are valid, nor would they be likely to value anonymity given the limited use of the coin (further, it's doubtful that corporations would want them to be anonymous - collecting user data is a major benefit for loyalty programs.

The main benefit I could see would be that users could potentially trade loyalty points amongst themselves - for example, if you pick up my dry cleaning on your way into the office, I'll send you enough Starbucks Points to buy yourself a latte.