The correct form is “video game” (with a space between “video” and “game”). This is the most widely accepted and standard usage.
Although “videogame” (as a single word) was once used, especially in older publications, most style guides and dictionaries now favor the two-word version, “video game.” This is the form you’ll see in formal writing, publications, and most online sources.
So, unless you’re following a specific branding or style guideline that uses “videogame,” it’s best to go with “video game.”
