Short answer

Yes, exiled cards are now in the game; so, no, "outside the game" does not include exiled cards anymore.

Long answer

According to the Comprehensive Rules:

400.1. A zone is a place where objects can be during a game. There are normally six zones: library, hand, battlefield, graveyard, stack, and exile. Some older cards also use the ante zone. Some casual variants use the command zone.

400.10. An object is outside the game if it isn't in any of the game's zones. Outside the game is not a zone.

108.5. Nontraditional Magic cards can't start the game in any zone other than the command zone (see rule 408). If an effect would bring a nontraditional Magic card into the game from outside the game, it doesn't; that card remains outside the game.

When you bring your deck into the game, it starts as your library. Cards then move to the hand, battlefield, graveyard, stack, exile, and ante zones during the course of play. There is (currently) no way for a card that has ever been part of the game to no longer be in one of these zones, so all of the cards in your deck stay in the game.

Note in particular that this changed during the Magic 2010 rules changes. Before then, the exile zone was called the removed-from-the-game zone, and was explicitly considered "outside the game." Given the number of cards moving things back and forth between that zone and the battlefield, R&D got fed up with its terminology. Given that "exile" doesn't feel nearly as outside the game, and the fact that certain exiled cards had significant in-game effects, they felt like weakening nine cards was worth bringing the zone fully within the game.

The command zone is only used for nontraditional cards (vanguard, plane, and scheme cards, at the moment). They're explicitly not allowed in any other zone, and are explicitly prohibited from being brought into the game mostly because nobody wants to deal with the consequences of Wishing one up.

For tournaments, the Magic Tournament Rules add a significant extra restriction in section 3.5:

Certain cards refer to “a (card or cards) you own from outside the game.” In tournament play, a card “you own from outside the game” is a card in that player’s sideboard.

The contents of your sideboard are governed again by the Comprehensive Rules:

100.4a In constructed play, sideboards are optional, but must contain exactly fifteen cards if used. The four-card limit (see rule 100.2a) applies to the combined deck and sideboard.

100.4b In limited play involving individual players, all cards a player opens but doesn't include in his or her deck are in that player's sideboard.

100.4c In limited play involving the Two-Headed Giant multiplayer variant, all cards a team opens but doesn't include in either player's deck are in that team's sideboard.

100.4d In limited play involving other multiplayer team variants, each card a team opens but doesn't include in any player's deck is assigned to the sideboard of one of those players. Each player has his or her own sideboard; cards may not be transferred between players.

Note that for games after the first in a match, if you have moved cards between your sideboard and your deck, "outside the game" refers to your current sideboard, not your original one.