The issue of what makes a group of stars a galaxy is an important one. With earlier observations, mostly larger galaxies were seen and general size and structure (core and spiral arms or elliptical symmetry) left little ambiguity. However, with the increasing discovery of smaller dwarf-type galaxies, it is becoming increasingly more difficult to determine between say a large globular and a small mass galaxy.
Dwarf galaxies were thought to have several billion stars, which still exceeds a large globular of several million stars. However, the globular cluster omega Centauri of some 5 million stars is considered a possible remnant core of a stripped satellite galaxy.
With the discovery of smaller satellites such as Willman 1, it is becoming more important to differentiate between structures which are either a globular or a low-mass galaxy. Willman 1 has been estimated to have as few as half a million suns.
http://en.wikipedia.org/wiki/Willman_1
Correct theories of evolution of the galaxy and its satellites have to account for the different modes of origin of different structures.
The paper is an interesting approach to involve non-professional people in research and discussion and could present some new insights. However, in the final analysis, it is up to the experts or professional to decide on the working criteria of a definition of a galaxy, which will probably change over time as new information comes to light.
Regards, Rob