Quick numbers check:
Author estimates over 200k galaxies in the image. Image covers 0.004% of the sky.
200000/0.00004 = 5,000,000,000 galaxies. (edited, thanks to % help from commenters below)
Finding somewhat standardized values for this rather standard question is frustratingly vague. Estimates range from a few billion to a trillion, though the most frequently quoted number I could find was about 100 billion.
The standard for measurement in the last 10 years or so have been the Hubble Deep Field Survey images. In the last one done, there were about 10k galaxies shown. The HDFS had a square arcminute resolution of 11.5. It would require 12,913,983 HDFS-type images to cover the entire side. (ref: http://curious.astro.cornell.edu/question.php?number=720)
Using these numbers: 12913983 * 10000 = 129,139,830,000 galaxies.
So why the vast difference between the two numbers? My supposition is the new ESO image isn't as deep as the HDFS.
I would argue the larger number, ~129.134 billion galaxies is a bit more accurate.
Damn, 129 billion galaxies. Someone else has to be out there.