Currently the use of this tag is ambiguous.

From the wiki:

This tag is used for any image or animation which shows a video game ¹, or a character who originates from a video game², as part of the scene.

The two usages, frankly, are radically different. I propose that we separate the tag into two subtags:

video_game for any post which features a depiction of a video game, such as a game disk, box art, console, etc
video_game_character for any post which features a character from a video game.

First of all, they should be singular, as is customary for tags describing an object. The second tag's name fits its purpose better than just "video games" does, which is why it should be evacuated from its current name.

But, there are also 500k results for it and dozens of implications, and separating the two represents an enormous amount of work... Is it worth it to try to fix this?

I think the tag is fine as is. Handhelds and consoles have their own line of copyright tags that implicate video games.
A video_game_character tag sounds redundant.

Honestly the video games tag does feel a bit overloaded, to me. Tags like Nintendo implicate it, yet Nintendo does own and control franchises and IP that aren't exclusively video games. Pokemon being a main example; there are characters and pokemon that originate from the anime or movies, but posts with them end up getting saddled with video games despite not showing a video game or a character who originates from a video game. Considering there are cross-media franchises that can include video games, tagging characters that come from said franchise as always being from a video game despite it not always being clear which media format they really originated from, seems wrong. It seems to me the tag is basically "any image or animation which is maybe sort of kind of related to a video game in some way".

On top of that, it does make it nearly impossible to search for posts that contain actual video games or video game-related paraphernalia, since the results will be dominated by posts with characters that have a relation to a franchise that includes video games.

But given the over half a million posts with the video games tag, I can't say I see a realistic option for dealing with it. Unless you were to remove the existing implications, nuke the current tag from all posts that have it, then adding more specific implications to specific tags (avoiding any wide brushes, like companies, or franchises that can span mediums). But as it is, video games is a pretty useless tag.

Controller and playing_videogame can help with finding paraphernalia etc... although they often include generic "gaming" rather than specific games.