One important point that the author seems to have misunderstood is that Borg was the predecessor to the other two systems, not the successor. Borg went into production (running a bunch of websearch dedicated clusters) in late 2004, long before Mesos or Omega were around. Omega is/was an experimental replacement for Borg that was started much later, although I'm not sure how much production load it actually took over.
Author here. I ordered them based on time of publication, and evaluated them based on the contents of the paper. My summary wasn't meant to be a substitute for actually reading the papers either, the Borg paper states that it started out as a centralized scheduler and has evolved over time, and also that it's been in production for over a decade. Clearly, it predates Mesos and Omega.
I've heard varied things about the use of Omega in production. The Borg paper mentions that it runs 98% of machines at Google, but that number is apparently dated. One person said that Omega runs all the batch work, and is being rolled out further. However, I've also heard it's being phased out.
I initially thought the same thing because the author commits this error in the opening act. But later he seems to understand that Borg absorbed the good ideas of Omega, and that Borg is the one that exists in practice.