You mean, you never decide what piece of puzzle to move or what object to use on certain area?

Well, you can choose which puzzle piece to move, but it of no consequence since you have to move them all to the correct place eventually.
In most adventure games you don't have much of a choice either (except the order again) because of you don't use the correct object in the correct place, the game just won't move on.
This is something that makes games like Maniac Mansion special - you can choose your "heroes" and depending on that, the solutions to puzzles change. And depending on what you do (give microwaved hamster to Ed) you can get interesting game-overs ;-)

But that's the whole point - you must choose correct action among all avaliable. Sure, you must do it only once, but that one time you are still choosing.

So anything that educate or train you can't be a game? Poker and other competitions, involving real money are not games too?

This is the deepest thought i've seen in a long time without warnings being dished out.

Why does GOG distinguish between Games and Movies then? Does that mean the movies offered here are not considered an amusing diversion? ;)

The boundary between symbolic categories will necessarily be fractal.
To illustrate my point, think of a one-dimensional number line (with all the counting numbers, for example, starting at 1, 2, 3, …, n). If we include zero, this set is called the Natural numbers.
Now, between each natural there are many numbers not included on this definitive line; fractions, irrational numbers, etc. In fact, how we determine the value of a number on the line is relevant. (Derrida, il n'ya a pas de hors-texte : there is nothing outside context [in which the fact is represented], 1967).
So, if we take a number as the decimal representation, for instance, to three decimal places, then the first number is 1.000. But any approximation (three decimal places approximates four and more orders of diminuitude) is inherently eliding some detail. So, the numbers between 0.445 and 1.444 are all represented by this single point on our hypothetical numberline.
There are holes between the numbers, and the holes are actually (thanks to Cantor, we can measure them) bigger than the numbers (i.e., there are larger sets of infinite numbers between the members of the infinite set of natural numbers).
This holey discontinuity illustrates (in a single dimension) a fractal boundary. The closer one looks at the boundary, the more detail is apparent. (You can extend the definition as far as required, to four, five or even four hundred decimal places, but still there are no limits to be found.)
This also explains what I mean by a fractal boundary between members of an abstract category taken from the infinite reality we swim in.
You may even trace the discussion back to Socrates and the eternal discussion of quiddity: Plato's Forms were a attempt to nominate a general thing from which all instances of a particular type could be determined. Aristotle thought such discussions only relevant for practical pursuit, so he adapted the concept as teleology (something is a game if its fun to play, he might have argued, for instance).
There is also the concept of gaming a system. This indicates that human cognition enjoys figuring out how stuff works, then testing this solution (gaining the reward of satisfaction when it works).

Something that I enjoy,immensely.

I would say that education is education even if it may look like a game from time to time and playing poker for money is a profession and doing it is working, not playing. But then, I never played anything to gain money from it.

Many games are creative and/or educational, they are not useless.
Many games are stressful, they are not leisure activity.

Some games just have no goal and no global success.

Evidently someone thinks stuffing raisins up their nose is a game. :P

If we only look at computer games and want to count kinetic novels as games (as well as things like Conway's Game of Life), we could make this distinction:

* If it is distributed as an executable file, or something similar (like a script), it's a game. (Maybe we should impose the requirement that the language be turing complete.)
* If it is distributed as some other type of file (like a movie file, for example), it is not a game.

Of course, like any attempt at defining "game", it may classify certain works in ways you don't expect. For example, a "demo" (from, for example, the Commodore 64 demoscene) would be a game, but a video of it would not be, despite the demo being completely deterministic and non-interactive.

Perhaps determinism and interactivity would make sense in a definition of game?

(Incidentally, I would consider computerized standardized tests, like the GRE, to be computer games, even though they are clearly not designed for entertainment.)