A gospel of salvation, as described only once in the Bible (Ephesians 1:13), is the good news of MY PERSONAL salvation (it is also good news that YOU are saved, but that is more important to you than it is to me). Salvation is good news. It is true, it is important. It is contained in the gospel. But Salvation isn't the "Gospel of the Kingdom" and it isn't the Gospel of Jesus.
A gospel of salvation focuses on SELF. MY personal salvation, MY personal Savior. The OBJECT of salvation is ME (MAN). The faith is MINE (even if that faith is a gift of the Spirit). There are only two verses in the entire Bible that contain both words, gospel and salvation. (Rom.1.16 and Eph.1.13) There is NO Biblical text (ZERO) in which the words preach and salvation both appear.
A gospel of salvation focuses on personal salvation in the future. In the sweet by and by, if I do the right thing(s), I will (eventually) receive salvation. I will go to heaven. The Gospel of the Kingdom focuses on Jesus having already come down and reigning NOW as KING. It arrived in the past (at the time of Christ's victory), it is present (Christ is reigning NOW in His Kingdom) and it is future (ending with the restoration of all things).
The Jews at the time of Yahushua (even His followers) incorrectly believed a Gospel of Salvation and incorrectly looked (exclusively) for a Redeemer.
Luke 24:21
But we trusted that it had been he which should have redeemed Israel: and beside all this, to day is the third day since these things were done.
Like the ancient Jews, Christians today incorrectly concentrate on a Redeemer (salvation), instead of a King (Christ's government, the Kingdom of Yahweh).
There is no question that salvation, the result of atonement through Yahweh, the Son (the current, heavenly name of Jesus) is true. In fact, it is the very HEART of the Gospel of Jesus. It IS what Yahweh, the Father did, and what was accomplished, through His Son, to reconcile and redeem us.
John 3:17
For Yahweh sent not his Son into the world to condemn the world; but that the world through him might be saved.
John 12:47
And if any man hear my words, and believe not, I judge him not: for I came not to judge the world, but to save the world.
The Gospel of the Kingdom is the "SEED" or "WORD" of Yahweh that will result in His great harvest (see Seed and Vine - Promise of Harvest). The correct doctrine of Salvation is the GERM of that seed. But the germ, planted by itself, will not grow. The entire seed must be planted to yield a harvest.
The doctrine of Salvation was NOT Jesus' GOSPEL. It was NOT the gospel that He preached and is NOT the gospel of the great commission.