Well, it's popular because it takes two very iconic and beloved characters and gives their relationship a new and unexpected dimension. People are always intrigued by different interpretations of existing relationships.
The short story in Tekken 7 could be due to various reasons. It might be to keep the game fast-paced and action-oriented, or perhaps resources were allocated more towards the graphics and mechanics.
It could be that you rush through the storytelling or don't spend enough time fleshing out characters and settings. Also, lack of diverse events or complications can make the story seem short.
Maybe the brevity was intentional to focus on a specific moment or emotion and make a stronger impact on the readers. Also, the story might have been designed to be a sort of snapshot rather than a detailed account.
It could be that you haven't explored all the possible subplots or character arcs. Also, the lack of descriptive language can make the story seem shorter than it could be.
Music is short on stories perhaps because it aims to communicate in a more abstract and intuitive way. It's about creating a feeling or atmosphere rather than laying out a full-fledged story. Plus, listeners' attention spans for a single musical piece might not be long enough for an elaborate story.
In some fanfictions, Vegeta could be under the influence of some external force. Maybe an evil entity has convinced Vegeta that kidnapping Goku is the key to achieving ultimate power. Vegeta, being power - hungry as he is, falls for it and kidnaps Goku. But later, he realizes his mistake and has to make amends, which can lead to an interesting story arc of redemption and friendship building between the two Saiyans.
Well, sometimes short stories focus on intense emotions or difficult situations to make a big impact in a limited space. That can often lead to a more depressing tone.