Mario's Bombs Away
The game involves Mario - a soldier in this game - on a mission to carry a bomb to his troops on the other side of the screen. The enemy is waiting on the trees in his path, so he must keep his bomb away from their torches. One of his comrades is the heavy smoker, who is a slacker that carelessly tosses burning cigarettes into a stream of spilled oil, so he must also keep it from igniting on the ground. When he reaches the other side, he must carefully pass the bomb to his buddy, who will toss it on one of the five trees. After five bombs are passed, they will explode on the enemy, rewarding the player with bonus points. The game ends when there are three "misses" (ie. Mario's own bomb comically detonates in his face as well as blows up his outpost). True to the game's wartime jungle setting, there is an alarm monkey serving as this unit's time function.
It was later re-released in its classic form in Game & Watch Gallery 4. It can be played after the player collects 100 stars.
Given the Jungle setting and the style of uniforms that Mario and the other soldiers are wearing, the war in question was presumably the Vietnam War.