If you buy a domain and don't renew, theres a ~45 day "redemption period", during which you can pay a fee to get it back (GoDaddy charges $80 for this). If you don't, the domain is released back into the wild by Verisign, and all registrars get an equal crack at it. The reason Pool has such a good chance is that they own 80 registrars, so they have 80 horses in the race. That's what the original article discusses.
However, in the last few years drop-catching has become largely irrelevant. Here's why, using GoDaddy and TDNAM as an example:
During that 45 day redemption period, GoDaddy auctions off the right to buy the domain via the TDNAM. If someone pays the fee, they'll renew it themselves to sell it, it never hits the wild again, and the drop catchers never get a shot.
This is how I got GeorgeWBushLibrary.com for $15 (paid TDNAM fee), which I then sold for $35,000 less than a year later.
Network Solutions has NameJet, enom has one too (forget the name). Between those 3, most domains are covered, making drop catching a dying art.
Edit: Its important to note that each aftermarket can only sell domains currently registered at their registrar. So TDNAM only sells domains regged @ GoDaddy, NameJet only sells domains regged @ NetSol, etc.