No, It does not mean "gospel" in the context of the verse you referenced. It is the name of Christ Himself
The word of God refers to the Gospel of Jesus Christ, as the context shows.
But they have not all
obeyed the gospel. For Isaiah says, “LORD, who has believed our report?” So then faith comes by hearing, and hearing by
the word of God. Romans 10:16-17
Same thing here: Context
To them it was revealed that, not to themselves, but to us they were ministering the things which now have been reported to you through those
who have preached the gospel to you by the Holy Spirit sent from heaven—things which angels desire to look into.
Therefore gird up the loins of your mind, be sober, and rest your hope fully upon the grace that is to be brought to you at the revelation of Jesus Christ; as obedient children, not conforming yourselves to the former lusts, as in your ignorance; but as He who called you is holy, you also be holy in all your conduct, because it is written, “Be holy, for I am holy.”
And if you call on the Father, who without partiality judges according to each one’s work, conduct yourselves throughout the time of your stay here in fear; knowing that you were not redeemed with corruptible things, like silver or gold, from your aimless conduct received by tradition from your fathers, but with the precious blood of Christ, as of a lamb without blemish and without spot. He indeed was foreordained before the foundation of the world, but was manifest in these last times for you who through Him believe in God, who raised Him from the dead and gave Him glory, so that your faith and hope are in God.
Since you have
purified your souls in obeying the truth through the Spirit in sincere love of the brethren, love one another fervently with a pure heart,
having been born again, not of corruptible seed but incorruptible, through the word of God which lives and abides forever,
because
“All flesh is as grass,
And all the glory of man as the flower of the grass.
The grass withers,
And its flower falls away,
But the word of the LORD endures forever.”
Now this is the word which by the gospel was preached to you.
1 Peter 1:12-25
We are born again through hearing and believing the gospel.
JLB