Very interesting, but entirely theoretical. We are not even sure what causes short gamma-ray bursts (under two seconds in duration). It is theorized that short gamma-ray bursts might be caused by the collision of two neutron stars, or two black holes, or a neutron star and a black hole, but not two white dwarfs because they have insufficient mass. However, no such event has ever been observed.
A white dwarf will have a maximum mass of 1.44 solar masses (see
Chandrasekhar Limit). The remnants of a star that is between 2 and 3 solar masses will produce a "strange" or "quark" star. Remnants of stars between 3 and 9 solar masses will produce neutron stars. Remnants of stars between 10 and 130 solar masses will produce black holes. It may also be possible, at least in theory, to generate a short gamma-ray burst if a strange/quark star collides with a neutron star or black hole.
Long gamma-ray bursts (more than 2 seconds in duration) are the result of very massive (and very dusty) stars when they go supernova. In such an event there would still be supernova remnants that we could see today. For example, the Indian, Arabic, Chinese and Japanese astronomers recorded a supernova in 1054 AD, which we can see today in the form of the Crab Nebula. SN 1054 was 6,500 light-years away, and visible during the day. So I agree with the article that it was not likely caused by a long gamma-ray burst within 3,000 to 12,000 light-years.
They are also basing their theory of a short gamma-ray burst on the assumption that the event was not observed and recorded. Considering that this supposedly occurred in 774 AD or 775 AD, it is not difficult to believe that astronomical events may be have been observed, but not recorded. A massive coronal mass ejection may also create gamma-rays, but it would also produce massive auroras which would have been visible for a couple days. An aurora of that size would have been visible in the lower latitudes on Earth (like the 1859 CME). I am not aware of any aurora being recorded prior to 1859. They certainly occurred, regularly, yet there is no written record older than 154 years.
I am not disputing their theory, merely suggesting that there may be other possibilities for gamma-rays hitting Earth than just a short gamma-ray burst from colliding dead stars or black holes. Considering the times, this was about three centuries after the fall of Rome, when Charlemagne ruled most of Europe. The "Dark Ages" began around the 6th century and lasted until around the 13th century, and astronomy actually lost ground during this period in Europe. So I consider it very possible that an astronomical event could have been observed (at least in Europe), but not recorded.
The article also assumes that there are no remnants of the collision (if a collision actually occurred), but considering the range they are talking about, between 3,000 and 12,000 light-years, that is a pretty big assumption. There may very well be remnants of dust and gas produced as a result of this gamma-ray burst that we have not yet detected.