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.
How do you "double-spend" that?
(I don't believe you really *can* but if you aren't a minter then you also can't guarantee that your message will ever get into a block so if you want to send such messages you now have an incentive to do the POW that your account's effectiveness requires)