Assuming that all their light is coming from stars, they have far too much stellar mass (with stellar masses similar to the Milky Way) to be the progenitors of today's globular clusters.
In globular clusters stars tend to have similar age in terms of main sequence progression. If most of the stars approach their brightest phase, the cluster will be extremely bright relative to its mass.
I've read the paper, those objects have all properties of AGNs, but since having AGNs so early doesn't fit current mainstream, authors try very hard to come up with a different explanation.