"that the viral envelope protein (E) binds to BRD2 and BRD4 and "potentially disrupting BRD-histone binding by mimicking histone structure." 

Thanks Bear.  You pointed out the hypothesized interaction is by disrupting BRD-histone binding so there goes the idea of some viral interaction outside of the BD regions.  I share your confusion - the virus seems to act as a BETi (competing with acetylated histones for BRD binding sites).  I also don't know what role apabetalone would play except maybe to knock the virus off the BD1 sites of BRDs by binding to the BD2 regions and changing configuration of the BD1 regions so the viral particles are knocked off or can't bind in the first place.  Why the virus binds to the BRDs at all (except perhaps to enable the BRD to directly interact with some host TFs such as NF-kB) is a mystery.

Jupe