Yes, the Gospel of the Kingdom, being under the administration of the Law of Moses, certainly required works, as the verses you quoted from John is saying.
The Gospel of the Kingdom is actually a good news found throughout the Old Testament. All Jews who study the OT are well aware of it.
Its the promise of a king that will come in the future thru the line of King David.
Jeremiah 23:5 KJV Behold, the days come, saith the Lord, that I will raise unto David a righteous Branch, and a King shall reign and prosper, and shall execute judgment and justice in the earth.
6 In his days Judah shall be saved, and Israel shall dwell safely: and this is his name whereby he shall be called, The Lord Our Righteousness.
Luke 1 NLT 30 “Don’t be afraid, Mary,” the angel told her, “for you have found favor with God! 31 You will conceive and give birth to a son, and you will name him Jesus. 32 He will be very great and will be called the Son of the Most High. The Lord God will give him the throne of his ancestor David. 33 And he will reign over Israel[c] forever; his Kingdom will never end!”
God's plan to establish the Messianic kingdom was no secret to the Jews of Christ's day. The kingdom is the very theme of Old Testament prophecy and is described there in great detail. Jeremiah 23 is to me, the clearest passage describing that good news (Gospel of the Kingdom)
Zechariah’s, father of John the Baptist, proclamation
Luke 1 (NLT)
68 “Praise the Lord, the God of Israel,
because he has visited and redeemed his people.
69 He has sent us a mighty Savior[h]
from the royal line of his servant David,
70 just as he promised
through his holy prophets long ago.
71 Now we will be saved from our enemies
and from all who hate us.
72 He has been merciful to our ancestors
by remembering his sacred covenant—
73 the covenant he swore with an oath
to our ancestor Abraham.
Note all the references in this proclaimation from Zechariah, who was filled with the Holy Spirit, was to Israel and the Jews. There is absolutely zero mention of the Gentiles.