Ex JW here. This is depicting one of the steps in their equivalent to the Rapture. It goes something like this:

• The UN activates as a full world government, and decides to destroy all religion (if you know the slightest bit about the UN, you can see how absurd this is before we get to anything else)
• After clearing out everything else, the UN suddenly realizes that Jehovah's Witnesses are still around
• They attack JWs (what OP's picture depicts), but God intervenes to protect them supernaturally
• Jehovah wins and tosses Satan in a deep pit
• Earth is transformed over 1000 years into a paradise. Nobody dies, and previous righteous people are resurrected.
• At the end of that, Satan is let out again for a final judgment of humanity
• Satan is killed off for good. Any human survivors live forever on a paradise Earth.

Gog of Magog comes from Ezekiel 38. From the New World Translation: "The word of Jehovah again came to me, saying: 2 “Son of man, set your face against Gog of the land of Maʹgog, the head chieftain of Meʹshech and Tuʹbal, and prophesy against him. 3 Say, ‘This is what the Sovereign Lord Jehovah says: “Here I am against you, O Gog, head chieftain of Meʹshech and Tuʹbal. "

Then, the term pops up again in Revelation 20: "7 Now as soon as the 1,000 years have ended, Satan will be released from his prison, 8 and he will go out to mislead those nations in the four corners of the earth, Gog and Maʹgog, to gather them together for the war. The number of these is as the sand of the sea."

So Gog is basically another term for Satan in this reading. Though Ezekiel seems to be talking about a people from a specific place.

As a side note, "But we can take comfort in knowing..." is a common phrase in their writing, and I get a little twitch every time I read it.