Alright, as @Naoki_Saten stated, I will be approaching this from the perspective of Game Theory. For those not familiar, it is a sub-branch of actually numerous topics, such as Economics and Computer Science. I actually took this course from Coursera: https://www.coursera.org/course/gametheory so those interested in further learning may want to take this one up It does look at things sometimes from a mathematical perspective, so be warned!
Anyway, to organize what I wrote on the chat, in Game Theory, the most simple way to describe a game is through Normal Form. In order to be able to describe a game through normal form, it must have the following:
- A finite number of players (VNs have 1)
- The actions the player can take (Which would be the choices in a VN)
- The "profiles" of actions of all players (Which is the list of actions made by each player)
- And a "utility function", given the strategy profiles of all players (Which is the ending of your VN)
If we were to classify a VN in normal form, then it could work as a game. The outcomes that result from the utility function give a certain "payoff" which could be the good end, bad end, true end, etc. Now, working with Game Theory isn't as simple as classifying these games. Here we can assign certain values to each outcome, say, 1 to good end, -1 to bad end, 5 to true end. Then we could attempt to calculate the optimal decisions that need to be made to reach the best outcome. Like if the player had to play some bad ends to reach the good end, we could single out the least number of bad ends needed to get the most payoff from his game. But a lot of that is debatable. Is assigning a negative outcome to a bad end really fair if the player himself wishes to see the bad end?
Furthermore, we could also classify VNs into separate games. Is getting into a character's route already an outcome? Then the route itself would be considered a new game. Indeed, for most VNs, once you get into a character's route, the choices you make in the common route have absolutely no effect on the rest of the route; only the choices made during the route affect the outcome. Of course, I can think of a few exceptions, like in CLANNAD and the goddamn Kappei route which required you to interact with Yoshino in common so that you could get the good end, but my experience tells me that isn't very common.
Now, I did a bit more research after the skype chat and found this resource: http://levine.sscnet.ucla.edu/general/whatis.htm which seems to imply Visual Novels fall more under Decision Theory. Although, most decision theory involves risks where there is a probability for the outcome to change despite your decision. Despite that, perhaps VNs would be more classified as "Decision Making" rather than "Game Playing"
Another resource here: http://assets.cambridge.org/052181/4626/sample/0521814626WS.pdf seems to assert that "A game must have two or more players, one of which may be nature." (p.4, under Terminology). The example it gives to a single player game such as Solitaire is that nature plays first by shuffling the cards.
However, in p.6, the author states that "Games of skill are one-player games whose defining property is the existence of a single player who has complete control over all the outcomes. Sitting an examination is one example. Games of skill should not really be classified as games at all, since the ingredient of interdependence is missing."
This seems to describe VNs right on the dot, because the single player has complete control over all the outcomes based on his decision. Therefore, if we use this author's words, then VNs "should not really be classified as games at all". And yet they are still called "Games [of skill]".
So, after all this rambling about Game Theory, what do I think? I think that the normal form that I described earlier is merely a way to convert Visual Novels into a means to be thought of from a mathematical perspective, which does not necessarily guarantee its status as a game. What it can do, on the other hand, is allow the player to devise an optimal solution to his desired outcome, which takes a lot of skill. Anthony Kelly (author of the book I linked above) does seem to describe it quite well with his explanation of "Games of skill" and that jives in with looking at games from the normal form. Any idiot can click and attempt every possible set of actions, but it takes someone with skill to decide what actions to take to maximize his own payoff.
But, as he said, they "should not really be classified as games at all"