OK, so tldr: If you can't define a partial ordering between events (ie. "earlier than" as in A can cause B, "later than" as in A can be caused by B, "same time" as in there can be no causal relationship between A and B), then time as defined in B-theory can't exist. So what? What are the consequences?
From the article, "[this] casts doubt on the reality of time in our world". If the order is undefined, then how can you say I'm late?
Or: it doesn't matter in which order you write the events of a story, as long as the events themselves are in order. The author is not bound by the timeline of the story.