What They Saw
They extracted DNA from A. vinelandii and E. coli and determined the amount per cell (by counting number of cells), finding that E. coli had about 3.4 femtograms per cell (3.4 * 10-15 g) and A. vinelandii had 135 femtograms. Assuming E. coli's genome is about 4 megabases (actually 4.6, though it depends on the strain) and it has only one copy per cell, A. vinelandii should have about 160 megabases-worth of DNA per cell. A. vinelandii's genome is only about 5.4 megabases, so that's about 30 copies of the genome per cell.
However, they made an artificial mixture of known numbers of copies of a certain gene in A. vinelandii and measured the intensity of radioactivity for the correct band of a Southern blot when probed with a probe labeled with radioactive phosphorus. The amount of radioactivity for DNA extracted from cells was about twice the amount seen with 40 copies of the gene, so they concluded there must be about 80 copies of the gene present. Does this mean there are 80 copies of the chromosome per cell? Not necessarily; there could be multiple copies of the gene per chromosome. However, I don't think that is the case.
They also tried with nitrogenase nifDK genes and got similar amounts of radioactivity. nifH gave multiple bands (presumably because of the alternative nitrogenases), but the main band gave a similar brightness.
To distinguish between a giant chromosome with 80 copies of each gene, and 80 copies of a smaller chromosome (or something in between), they integrated a resistance marker in a particular place in the genome. If it were a single large genome, the marker would probably only integrate once or a few times, whereas after several generations, the cell would make copies of a smaller genome with an integrated marker such that the amount of marker would increase over time. They observed the latter result, suggesting single copies of genes on a chromosome with many copies.
What This Means
The copy number of Azotobacter chromosomes was about 30-40 compared to E. coli but about 80 in terms of specific gene copies. A possible way to reconcile this is that the E. coli cells might actually have had more than one copy too. In any case, this many copies of the genome might make it difficult to stably transform the organism.