There's a lot to this situation that puts the Watchtower in a bad spot. The Watchtower states Christians must stay out of politics because, by voting, a person is saying they believe that human government can help mankind. As such, it is in a sense saying "We don't need God."
Yet, Jesus, and even the Watchtower, tells people to 1. Be in subjection to "earthly authorities" and 2. pay taxes. Taxes are the lifeblood of human government. Paying your taxes supports government at least equally as voting. Try going to your local body of elders as one of Jehovah's Witnesses and tell them you don't pay your taxes. Just see what happens. At a minimum you will lose every "privilege" you have in the congregation.
Next we have the concept that a person who does not vote is basically stating "Whomever wins the election is the candidate I support". This is an argument used by persons politically active. The Watchtower might say something like "Correct! No matter who the elected candidate is, we obey them as long as they do not ask us to violate God's commandments. We obey any law passed the same way." Great! So what happens when there is a candidate running for office or a voter ballot initiative that has legislation stating that there will no longer be tax exemptions for religious organizations?
Finally, what about all the letter writing campaigns the Watchtower asked it's member to participate in regards to the Russian ban on Jehovah's Witnesses? Add to that all the lawsuits the Watchtower uses to fight governments such as the Australian Redress Scheme? Why didn't the Watchtower simply obey rather than use the government (the courts) to fight such things?