PSP vs. Nintendo DS

I don't like to call the stuff on the DS games
They aren't (with the exception of Mario related stuff)
Best selling games for DS are things like brain training, cooking mama, nintendogs
All of which are not games

what are they then?

1. An activity providing entertainment or amusement; a pastime: party games; word games.
2.
a. A competitive activity or sport in which players contend with each other according to a set of rules: the game of basketball; the game of gin rummy.
b. A single instance of such an activity: We lost the first game.
c. games An organized athletic program or contest: track-and-field games; took part in the winter games.
d. A period of competition or challenge: It was too late in the game to change the schedule of the project.
3.
a. The total number of points required to win a game: One hundred points is game in bridge.
b. The score accumulated at any given time in a game: The game is now 14 to 12.
4. The equipment needed for playing certain games: packed the children's games in the car.
5. A particular style or manner of playing a game: improved my tennis game with practice.
6. Informal
a. An active interest or pursuit, especially one involving competitive engagement or adherence to rules: "the way the system operates, the access game, the turf game, the image game" Hedrick Smith.
b. A business or occupation; a line: the insurance game.
c. An illegal activity; a racket.
7. Informal
a. Evasive, trifling, or manipulative behavior: wanted a straight answer, not more of their tiresome games.
b. A calculated strategy or approach; a scheme: I saw through their game from the very beginning.
8. Mathematics A model of a competitive situation that identifies interested parties and stipulates rules governing all aspects of the competition, used in game theory to determine the optimal course of action for an interested party.
9.
a. Wild animals, birds, or fish hunted for food or sport.
b. The flesh of these animals, eaten as food.
10.
a. An object of attack, ridicule, or pursuit: The press considered the candidate's indiscretions to be game.
b. Mockery; sport: The older children teased and made game of the newcomer.
v. gamed, gam·ing, games
v.tr. Archaic
To waste or lose by gambling.
v.intr.
To play for stakes; gamble.
adj. gam·er, gam·est
1. Plucky and unyielding in spirit; resolute: She put up a game fight against her detractors.
2. Ready and willing: Are you game for a swim?
Idioms:

i think they fall in there somewhere

Not in the traditional sense really
Nintendogs is not Halo

but it is still a game by definition