Homer mispronounces the word gym. This episode came out in 1998, Kamen Rider Gaim came out in 2013.
Ho Yay: Homer going into fanboy mode over Rainier Wolfcastle. "Oh I love your movies and your powersauce bars and your taut... rippling..." Rainier interrupts him before he can finish.
Memetic Mutation: "Look how far I climbed! And I don't even feel tired" explanation Said by Homer when he wakes up and sees how high he's into the mountain, not realizing that the two sherpas climbing with him have been carrying him upwards during the night while he was asleep. This scene is often used to mock people who (obliviously or otherwise) take full credit for something that was mostly or entirely done by other people (such as, for example, millonaires who were born into wealth and privilege yet claim that no one gave them anything and that all their money comes exclusively from their own hard work)