It's not that surprising, then, that Donkey Kong was conceived as a Popeye game. And it's even less surprising, considering the runaway success of Donkey Kong, that Nintendo was able to secure the rights to the property for a subsequent game.
Popeye the arcade game (and NES game, to maintain the pretense of Virtual Console eligibility) is strikingly similar to Donkey Kong, in that a character flails around, avoiding his nemesis, in order to rescue the girl. But if it's possible for a licensed arcade game to be weirder than Donkey Kong, Popeye is. While Jumpman/Mario saved Pauline by actually contacting her or incapacitating Donkey Kong, Popeye's objective is to catch falling hearts, musical notes, or the letters H-E-L-P as they waft downward from Olive Oyl.
All I can think of is that by performing actions that directly react to her feelings and calls for help, making sure to address every one (you can't let them fall to the ground or into the ocean), what Popeye is doing isn't so much rescuing Olive as reassuring her -- except that catching the letters causes a ladder to spontaneously grow. How uncharacteristically sensitive for a guy who spends most of his time trying to impress Olive with feats of brute strength. Meanwhile, Bluto (or Brutus, as he was known at this time) walks around the stages menacing Popeye, and the Sea Hag, a generally forgotten Popeye character, throws bottles at Popeye.
Popeye, though unusually passive in response to Olive's despair, is still capable of exploding into a spinach-fueled berzerker rage. When he's on spinach, Popeye can send Brutus flying around the stage, incapacitating him temporarily. Even without spinach, Popeye can punch, but this is more useful for picking up spinach than anything else.
It seems unlikely that Nintendo would even try to reacquire the rights to Popeye for the Virtual Console, but the game is historically important enough in my mind to be worth the effort. Popeye was one of only three launch games for the Famicom, along with Donkey Kong and Donkey Kong Jr. And, somehow, Namco got the rights to both the Popeye license and Nintendo's original design for a mobile remake. If they can do that, than certainly Nintendo can convince King Features to let them use the character. It's not like it's a sought-after franchise or anything. When was the last time you even thought about Popeye? He may be nearing the finich until which he is strong because he eats his spinach.