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I talk about FPS in this case :
Play Bioshock,Far Cry,Crysis
to know what is a fun and higly enjoyable game.
-top graphics with normal/specular maps and lights : no more flat textures and
old flat lightening
-lot lot of effects from shooting,smoke,water
-some physics to play with for pleasure and things to destroy/break
-improved gameplay and camera movement during running,shooting
-liberty of achieveing a goal liek you want by several ways (Deus Ex game base )
....
i played Metroid 3 on WII , it is far far from the fun and graphics of these PC
games.

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Before I read your points, I tried to think of the things that make FPS-Games enjoyable for me. Of course, I am not a big fan of these kind of games in the first place, but it should still be noted that I did not think of the graphics, even though they play a big part in FPS games.
Instead of dozens of shaders or very high texture resolutions, it's more about the polish of the whole game and how it all comes together. I can still enjoy games that are a few years old, even though they don't have "to graphics with normal/specular maps...". It can't be only the graphics, I suppose. They play their part, but nowadays it's more about the art and how it all comes together and the level of polish. Expectations rise these days, so maybe games now have to have all these shaders, I don't know. But is this really what makes these games "fun" or, to go back to the thread, "games"?
(I also disagree about Metroid Prime 3, I have great fun playing it, and the level of polish in there is amazing)

Let`s have a look at the other points you mentioned. Other than graphics issues, you mention a physics engine. Yeah, it's fun when the crates (speaking of which, there are way too many crates in videogames) fall realistically, but is this really so important? Half-Life 2 showed that it can be enjoyable and cna be cleverly incorporated into games, but I don't think that this is a must-have-feature (although I suppose physics in games will become a standard in the near future).
"Improved gameplay" is a clever point, because you basically circumvented the question we try to answer here! What is gameplay, at its very basic core? What concept is behind that? And how can you improve that? Would be cool if you could elaborate on that
The nonlinearity and possibility to solve goals in several ways is also a cool feature, but by no means is it something that divides between "game" and "not-game", which is what we discuss, if I understand the question right.

If I were to mention games like Phoenix Wright, games that do have their fans (like, you know, me), then we would have to see that it doesn't even fulfill one of the goals you mentioned. Fair enough, thats not a FPS, but it is still a game (although some may even argue with that).

What makes a game a game is, for once, the interactivity. Of course, the player, the user, can interact with the game, their characters, their weapons or whatever it is the game presents. It can be as simple as flipping blocks (Tetris) or changing their colors in puzzle games, or as complex as moving a virtual avatar through a world, interacting with thousands of other players (MMORPGs). The level of interactivity is different, though, and what you are doing.

Looking at the article I've posted, especially at the very first chart, we see that games are compromised of several game mechanics, little things to do with specified rules that, when done, change something in the world and provide feedback. This then changes other aspects in the game, unlocks new ways to spend your time (maybe other game mechanics, or other parts of the map). When you look at it, many games can be broken down into several "minigames" that are actually quite simple. In a shooter game, you could have the minigame "move", "look around", "aim" and "shoot". Only put together are these interesting enough for the most hardcore of players (and even then, they want many different things to happen), but for newcomers to videogames, this can be a very difficult concept to grasp and understand, let alone master.
My beloved Phoenix Wright is much, much simpler, with the parts being investigating (verbs are: investigate, move, talk and present), dialog/in-court (which is pretty much a "select what you want to do now"-kind of thing) and cross-examination (find the lie, show the proof). It's much, much simpler than the shooter mentioned above, and there are not as many things to do at once. Maybe this is why its easier for newcomers to play that.

I've now written a lot. Nobody will probably read this far. Too bad, I guess.

@JulzMighty: It was quite interesting to read what makes you reply to a Showcase-post. I think that a "how-to-present-a-game"-thread would be quite interesting as well Someone should totally open it.