Note how John explains for whom Christ died in the context of 1 John 4:9-11, 14:
1 John 4:9 This is how God showed his love among us: He sent his one and only Son into the world that we might live through him.
1 John 4:10 This is love: not that we loved God, but that he loved us and sent his Son as an atoning sacrifice for our sins.
1 John 4:11 Dear friends, since God so loved us, we also ought to love one another.
1 John 4:14 And we have seen and testify that the Father has sent his Son to be the Savior of the world.
Observe how John specifies for whom Christ died: "God showed his love among us," "that we might live through him" (1 John 4:9), "he loved us" and he is "an atoning sacrifice for our sins" (1 John 4:10) "friends" since "God so loved us" (1 John 4:11).
We might add that John 3:16-17 is not in disagreement with this interpretation. It reveals two things: (1) that God sent Christ in order to save "everyone who believes" (John 3:16) and (2) that God sent Christ in order to save the world (John 3:17).
The first point is not so clear in most translations. The Greek, however, is quite clear. It identifies a specific group of people whom God sent Christ to save, and it labels them "all the believers" (pas ho piston). Greek does have a way to say "whoever" (hos tis), but that is not the language used here. More literally, the text ought to be translated something like: "in order that everyone who believes in him should not perish." Older translations often render the verse in this way (e.g. Wycliff [1380], Tyndale [1534], Geneva [1557], Rheims [1582]), as do modern versions such as the NRSV. The same is true throughout this passage (e.g. John 3:18). In other words, neither in John 3:16 nor anywhere else in this context does John state that it was God's intention to make salvation possible for everyone, or to save an undefined group of people. Instead, he states that God's purpose was to save all the believers. Clearly, a universal atonement is not necessary for the accomplishment of this purpose. Rather, the fact that God's purpose was limited to saving believers actually strengthens the case for limited atonment by demonstrating that it was never God's intention to save everyone.
The second mention of God's intention in sending his Son is found in John 3:17. There we see that God sent Christ in order to save "the world." For more on this see "For God So Loved - John 3:16-21" below. See "Definite Atonement: For Whom Did Jesus Die?" below.
God sent his one and only Son… the propitiation. God reveals himself by sending his unique, dearly loved son (see notes Rom 8:32; cf. Gen 22:12). By living in accord with God's will, laying down his life, and being raised in vindication, Christ is qualified to give life to God's people. To live in the fullest sense, according to John and the rest of the Scriptures, is to love God and other people fully, that is, in the same way that Jesus loved. On propitiation or atoning sacrifice see note on 2:2.