Actually they finally managed to get their hands on it as of May 13, 2015.
http://tmsearch.uspto.gov/bin/showfield?f=doc&state=4807:ud3p30.2.1
Watchtower withdrew their petition to cancel JW Player's trademark because the two parties had entered negotiations to settle, and apparently this is the result. Who knows how much they paid out. Look for a little "R" to appear in place of the "TM" on the JW.ORG logo just like it does next to Watchtower and Awake on the inside covers of the magazines.