This is interesting. In my undergraduate biology courses we worked using the three domain model (Archaea, Eukaryota, and Bacteria) and my understanding was the superkingdom or empire view was antiquated. I didn't realize there was still research or debate about the organization of life at the highest level.

I'm a bit confused as with the three domain view, it is informed by genomic analysis (specifically of highly conserved tRNA which all life appears to have, review paper here, and a link to a more recent tree of life which I am familiar with here) which is an empirical grounding through raw data instead of the models proposed which don't seem to have as comprehensive of a backing.

Newer tree of life below:

I wonder if it'll be like the definition of species where there are several criteria kept and used depending on the context. It's hard to imagine since all of the different methods of classification could be used fruitfully without relying on them as higher level classifications. For example the two superkingdoms mentioned in the paper you linked works well enough with Gram-Positive and Gram-Negative diagnostic tests and any exceptions would warrant individual study without necessarily needing to rely on some higher order organizing principles at least at present.

As an aside: I read on Wikipedia that Ernst Mayr didn't think the three domain model made sense :/ I wonder what his reasoning was... Something that I encounter is the great personalities and thinkers being kinda on the wrong side and wishing they were right since I think they are kinda cool. I think the same applies to Stephen Jay Gould and his idea of Punctuated Equilibrium.