I think that's enormously underrating the ability of viewers to engage with sci-fi. The prank itself involved a completely fantastical concept (transporters), which obviously doesn't make it less comprehensible/relatable to viewers; there's no reason that character dialogue and gestures can't be similarly rooted in the show's fictional universe, and it'd probably be funnier if they were.
The episode even already succeeded at it with the Vulcan bully - the "attention cadets, we have done this because it is fun, and will continue to do it" taunt was genuinely funny in blending Vulcan stoicism with the high school bully persona the script was going for. Jay'dens reaction, similarly, relied on Klingon honour culture, and was more amusing for it. There's a lot of fun you could have with the idea of a Romulan jock.