In English "the" refers to a specific item or multiple specific items. "The video game is a fun activiy," refers to some specific video game. "The video games are a fun activiy," refers to some specific video games. In English we can us the plural and leave off "the" to make it more general - about all of those things, not specific ones: "Video games are a fun activity.
In Hawaiian, you cannot leave off "ka" unless you are using some other determiner. Every noun must have some kind of determiner. Thus to talk about video games in general you still have to use "ka". Sometimes that means that without context you can't tell if the sentence is talking about a specific item or generally talking about those items.
Theoretically this sentence could be either "Video games are a fun activity" or "The video game is a fun activity", but the second sentence (the one you suggest) is an odd sentence in English. We would be more likely to say, "That video game is a fun activity." I can see why the Hawaiian team decided not to accept "The video game", though, since it is a grammatical sentence and a direct translation, I would probably be inclined to include it if I were making those decisions.