It is certainly true that valuing the PoW expended by the miners is essential for knowing where the break even point for a double spending attacker is. I.e. the point at which what they gain from the double spend == their lost block reward from orphaning their original blocks.
If the reward is not in the form of a "coin" then I'm not really sure that "double spending" applies at all (as that is dependent upon there being a "coin" is it not?).
Let me suggest a hypothetical example where the "reward" is simply the ability to send an encrypted message (via the block chain) to another account.
Bitcoin uses the block reward partly to incentivise miners not to double spend, because they stand to lose their block reward attempting to orphan the best block. If you have a non coin based reward, I'm not sure the same can be said.