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This took me down a rabbit hole. No pun intended given male Nidoran are somewhat based on rabbits.
I think that icon in the screenshot representing the Nidorans is most visually reminiscent of Nidoking and Rhydon. Probably Rhydon. It always felt more linked to Nidoking for me though. You can obviously get Nidoran much sooner in all three games. But all three members of the line are also represented by this icon. Whereas Rhydon merely adopted it after Rhyhorn was originally represented by the one for Rattata in that screenshot. Interestingly Rhyhorn is one of only three Pokemon (the others being Slowpoke and Magikarp) to change their icon upon evolution in RBY.
Anyway that monster icon represents
59 total Pokemon in RBY. No other icon represents more than 15. And you do tend to see these icons a fair amount - to switch your party order, swap Pokemon in battle, check stats, teach TMs/HMs, use HMs in the field, use potions/vitamins, etc. It even represents Mewtwo in Cerulean Cave in the overworld as a pseudo "final boss". Also represents other icons like Charizard, Gengar, and Snorlax (also in the overworld).
So you're seeing this icon a lot. Which kind of subliminally (if unintentionally) drives Nidoking home as an iconic Kanto Pokemon. He's almost by definition iconic to RBY.