There are a couple of things that Jesus may have meant. Clearly John was a true prophet of God, and a great one at that. Jesus' language suggests that John was at least as great as Abraham, Moses and David, and perhaps greater. If we read it too literally, we will even think that John was greater than Jesus himself! Personally, I think Jesus may have been speaking in hyperbole (as was fairly typical) in order to emphasize the fact that the kingdom he was bringing would radically change things for the better. Alternatively, Jesus may have been referring to the still future stage of the fullness of the kingdom that we will experience when he returns, rather than to the present state of the kingdom.

At any rate, I like your first sentence of summary. But your second sentence is a bit too narrow, in my opinion. Certainly the atonement is part of what Jesus accomplished in his earthly ministry, and his earthly ministry inaugurated the kingdom, but the point in Matthew 11:11 is more directly related to the kingdom as a whole than to the specific blessings of the atonement. John and the other Old Testament saints were saved by Jesus' atonement, just as we are today, even though they "looked forward" to it, as it were. So, forgiveness was not new for them. What was new was the way Jesus was restoring the fallen kingdom of Israel, and bringing great blessings with it. The blessings Jesus mentioned explicitly were: healing for the blind, lame, deaf and lepers; resurrection of the dead; and the gospel preached to the poor (Matt. 11:5-6). Of course, these kinds of things also happened in the Old Testament, but not to the degree they happened once Jesus came, and certainly not to the degree to which they will be realized when Jesus returns.

If those of us living in the present time are greater than John, then it is because we live in the time when the age to come has been inaugurated (cf. this Q&A), a time when all believers are gifted by the Holy Spirit (cf. this Q&A). If we are greater, our greatness is in the degree of blessing we have received, particularly through the ministry of the Holy Spirit, but also through the current state of the kingdom.

I am inclined to suspect, however, that Jesus referred to the fullness of the kingdom, as it will exist when he returns. It seems to me that before that time, the least of us receives fewer blessings and less gifting than John did. The present age of sin and death is still a reality, and it hits some of us pretty hard. But after Jesus returns, even the least of us will be more blessed and gifted than John was in his day.