Honestly "Dark matter is also believed to interact with ordinary matter in ways other than gravitational." is wishful thinking. Why? We have no a priori reason to believe that matter must have multimodal interactions, and there is potentially a real ontological crisis. If dark matter only interacts gravitationally - which even people who don't "believe in dm" must accept is a possibility, them dark matter is unfalsifiable, so we have to be ok with the possibility that there is something in the universe that exists but we cannot ever satisfactorily argue that it does. LCDM advocates know that they are on philosophically shakier ground if that's the case, but aren't brave enough to admit it because they are afraid it weakens their main cause by association (to be fair it does, we should probably be exploring other explanations first)
> We have no a priori reason to believe that matter must have multimodal interactions
No, but as a posteriori reasons go "everything else couples to the weak force" is a pretty good one.
> them dark matter is unfalsifiable
Only insofar as all the ontological content of a physical theory are unfalsifiable: you can always shift complexity around between state and dynamics if you're willing to pay the price in elegance. Consider Kaluza-Klein theory, for instance. In some sense this demonstrates that classical electromagnetism is unfalsifiable - but no one actually cares.