What is a "real" video game?

I recently bought on Steam a visual novel type game named Cho Dengeki Stryker. I like the genre when it's well done. I have played several ones, but one prominent example is 9 Hours - 9 Persons - 9 Doors for the Nintendo DS, which is an excellent example of a visual novel that takes great advantage of both the genre and the platform to present a story-heavy game that's interesting to play. Thus I was looking forward to Cho Dengeki Stryker given the positive reviews it has on Steam.

This game, however, is different. It's a visual novel. Literally a visual novel. It's not just a game of the genre, but a literal visual novel. In other words, text with images, some animations here and there, and basically nothing else. You simply click the mouse to advance to the next paragraph of text, and that's it. It's fully voice-acted (in Japanese), but it's still just a novel.

This was quite a disappointment because this isn't, in fact, a game at all. There are no choices, no interactivity, no branching storylines to speak of, no gameplay, no puzzles, nothing. It's just a novel.

The distinction between these two categories of visual novel are more emphasized in Japan, where pure visual novels are distinguished from so-called "adventure games", which use the same style but involve actual gameplay (often in the form of some kind of puzzles) and, most often, branching storylines and/or non-linear (or out-of-order) storytelling depending on player's choices. However, the distinction is not very clear in the promotional material of the games when published here.

This got me thinking: What exactly makes a video game a "game"? Why do I consider Cho Dengeki Stryker "not a game" but 9 Hours - 9 Persons - 9 Doors one?

There ought to be some very basic elements to a video game to make it an actual game, as opposed to simply the equivalent of a novel or a movie.

Firstly, interaction: The program must be interactive in some manner. And this interaction should go a bit further than to simply wait for the user to click to advance to the next paragraph of text.

This is tightly tied to the second feature: Choice. The player needs to be given some kind of choices, no matter how primitive, rather than the events on the screen happening in the same manner completely regardless of what the player does. This could be, for example, choice of direction of movement, or choice of dialogue. Even if these choices have no grand-scale consequences to speak of, the mechanic should still be there.

Thirdly, a goal: A game should have some kind of goal that the player strives toward. It's not a question of how complicated or large that goal is (it could be extremely primitive and simplistic), but there should nevertheless be something that the player is trying to achieve, which is the point of the game. (This doesn't mean that the game must have an ending. A game could very well be endless, such as trying to play for as long as possible, with progressively increasing difficulty. The goal in this case could be, for example, trying to achieve the highest possible score.)

Fourthly, challenge: Achieving said goal should not be completely and absolutely trivial. This ties to everything above: Achieving the final goal ought to involve player choices, and those choices should be even slightly challenging. It should be something more complex than simply "click to advance". (This doesn't mean that the game has to necessarily be difficult and require great skill or knowledge. Even a very easy game can still be fully considered a game.)

Cho Dengeki Stryker has none of the above features, which is why I don't consider it a game at all.