The authors are supposing that dark matter at this stage of the universe has its own particles and antiparticles and they are annihilating each other, the energy released by that annihilation is generating the heat.
But if the DM runs out, then you'd expect the same to happen for non-DM matter, which it doesn't.
Just like a neutral atom can have a neutral antiatom.
As for why dark antimatter/matter pairs would persist longer rather than run out (I guess that's the opposite of what you're saying, but it's important to remember what we're seeing even looking back this far is way after the normal matter/antimatter annihilated immediately after inflation), it's effectively the same reason dark matter doesn't clump and retains it's roughly spherical form at larger than entire visible galaxy sizes. Regular matter interacts via the electromagnetic force, which has an infinite interaction radius. Charged particles repel and attract each other from large distances. Thus, fundamental particles don't need to get that close to each other to form atoms and molecules. Dark matter only interacts via the weak force, which has a tiny interaction radius. The fundamental particles need to more or less make a direct beeline to the same point in spacetime to ever touch each other, which has an extremely low probability of ever happening. It's the same reason Earth can be bombarded nonstop with unimaginably large numbers of neutrinos every second from the sun, yet virtually all of them go straight through everything. All of space is mostly empty space, even things that look solid to us because the wavelengths we can discriminate are much larger than the spaces between atoms and molecules. It wouldn't look that way to dark matter. It would look actually empty.
And gravity, or so I'm told.
But both gravity and the weak force are fields, and so just like EM, they pervade space. Isn't that right? The weak force weakend dramatically with distance, but it doesn't disappear - I thought one property of a field is that it pervades spacetime.
Not that that makes any difference to your argument.
As for the weak force, I think that's not necessarily a known property of DM, but rather a property of hypothetical candidates for being the dark matter known as WIMPs(weakly interacting massive particles).