Two versions of it two.
The first is from that gif you replied to. It was made during the period between the World Wars. Before The horror of Nazis, Flame Throwers, and Atom Bombs reared it's heads. Folks figured the end would have come from what seemed at the time (during WWI) as an endless War that would destroy all life on earth. Chemical Warfare was considered the biggest horror out of all asides from the brutal Trench Warfare.
The second version of this short was made by Hanna Barbera after WWII. It leans a bit more on the religious side than the first one, which the story being told to mouse choir boys by their Priest. It's more or less the same as the first but includes the new horrors that were streamlines for WWII. Advanced tanks, Flame Throwers, Shock Troopers, and of course, The Atomic Bomb.
It's interesting to see two unique periods of history clearly shown between the two shorts. One was based on a time that never thought a second World War would happen and were already trying to get over the horrors of the first Great War. The second was created during a time of fear when one bomb could decimate a whole city as shown by Hiroshima and Nagasaki. The fear escalated by The Cold War and the USA and USSR both making more bombs, making them more complicated (ICMB's, though the short showed the original A-Bombs dropped from traditional Bombers), and most importantly, making the resulting explosions Bigger!
The second short was made in 1955, though I feel it was one of the rare shorts, at the time during the Atomic Age when folks were enamored by the idea of Atomic power, to think about what "Atomic Warfare" truly means on a global scale, should WWIII ever occur.