They propose an interesting distinction but I think it's a false one. Arguments about policy are almost always relativist, and should be. Arguments about reality are generally objective. Political arguments, in a perfect world, should revolve around policy. There shouldn't be a fundamental debate in our society about verifiable facts - say, that HIV causes AIDS, or that anthropogenic climate change is a reality, or that leggings are not pants. The debate should revolve around how to project forward the best policy that appropriately balances all of the competing priorities. That's somewhat objective (i.e. you can get better projections of the effects of a policy through detailed modeling and retrospective studies), but mostly subjective (how do you weigh the relative importance of competing priorities?). Policy exists as a dialectic, where the ideal outcome exists in tension between multiple opposing viewpoints.
When people resort to arguing about facts, they're really saying that they are unable to marshal a coherent policy argument. Sure, it's entirely valid to argue about semantic overlays on facts (when does a 'human' life begin? Do jeggings count?), but the underlying truth is undeniable. As such, it's almost never worth engaging in a dispute with someone about facts unless they genuinely appear to be mistaken and open to correction (or, conversely, if you are not certain that your handle on the facts of a given situation is complete).
I personally think the problem is that people think they're arguing about facts (and that they're right), when in fact they're arguing about some sort of semantic overlay. If two political opponents are using similar terminology in fundamentally different ways, or interpreting the same data set to mean wildly different things, they think they're arguing about facts, when in fact they're just arguing about language and meaning. This means they have the cognitive challenges associated with 'arguing to win' in an objectivist mold but don't actually achieve anything because they don't understand what their opponent is saying.
Sometimes, all you need in order to at least understand one's political opponents is to agree on a set of common definitions. You won't necessarily have the same policy positions, but at least you won't argue with them over what is literally semantics. Most of the debates on Facebook - and, indeed, here - are at their core definitional in nature.