Prof. Robert L. Dabney writes extensively and very deeply. You can't take one section and lift it from the whole and make it seem something Dabney did not teach. The following is from Chapter 35 of his Systematic Theology:
"Conclusion.
This seems, then, to be the candid conclusion, that there is no passage the Bible which asserts an intention to apply redemption to any others than the elect, on the part of God and Christ, but that there are passages which imply that Christ died for all sinners in some sense, as Dr. Ch. Hodge has so expressly admitted. Certainly the expiation made by Christ is so related to all, irrespective of election, that God can sincerely invite all to enjoy its benefits, that every soul in the world who desires salvation is warranted to appropriate it, and that even a Judas, had he come in earnest, would not have been cast out.
But the arguments which we adduced on the affirmative side of the question demonstrate that Christ’s redeeming work was limited in intention to the elect. The Arminian dogma that He did the same redeeming work in every respect for all is preposterous and unscriptural. But at the same time, if the Calvinistic scheme be strained as high as some are inclined, a certain amount of justice will be found against them in the Arminian objections. Therefore, in mediis tutissime ibis . The well known Calvinistic formula, that "Christ died sufficiently for all, efficaciously for the Elect," must be taken in a sense consistent with all the passages of Scripture which are cited above."
Dr. Dabney goes on to explain in what way the atonement concerns every individual, elect and non-elect.
"God’s Design and Result Exactly Co Extensive.
There is no safer clue for the student through this perplexed subject, than, to take this proposition; which, to every Calvanist, is nearly as indisputable as a truism; Christ’s design in His vicarious work was to effectuate exactly what it does effectuate, and all that it effectuates, in its subsequent proclamation. This is but saying that Christ’s purpose is unchangeable and omnipotent. Now, what does it actually effectuate? "We know only in part," but so much is certain.
(a.) The purchase of the full and assured redemption of all the elect, or of all believers.
(b.) A reprieve of doom for every sinner of Adam’s race who does not die at his birth (For these we believe it has purchased heaven). And this reprieve gains for all, many substantial, though temporal benefits, such as unbelievers, of all men, will be the last to account no benefits. Among these are postponement of death and perdition, secular well being, and the bounties of life.
(c.) A manifestation of God’s mercy to many of the non elect, to all those, namely, who live under the Gospel, in sincere offers of a salvation on terms of faith. And a sincere offer is a real and not a delusive benefaction; because it is only the recipients contumacy which disappoints it.
(d.) A justly enhanced condemnation of those who reject the Gospel, and thereby a clearer display of God’s righteousness and reasonableness in condemning, to all the worlds.
(e.) A disclosure of the infinite tenderness and glory of God’s compassion, with purity, truth and justice, to all rational creatures.
Had there been no mediation of Christ, we have not a particle of reason to suppose that the doom of our sinning race would have been delayed one hour longer than that of the fallen angels. Hence, it follows, that it is Christ who procures for non elect sinners all that they temporarily enjoy, which is more than their personal deserts, including the sincere offer of mercy. In view of this fact, the scorn which Dr. William Cunningham heaps on the distinction of a special, and general design in Christ’s satisfaction, is thoroughly shortsighted. All wise beings (unless God be the exception), at times frame their plans so as to secure a combination of results from the same means. This is the very way they display their ability and wisdom. Why should God be supposed incapable of this wise and fruitful acting? I repeat, the design of Christ’s sacrifice must have been to effectuate just what it does effectuate. And we see, that, along with the actual redemption of the elect, it works out several other subordinate ends. There is then a sense, in which Christ "died for" all those ends, and for the persons affected by them."
http://grace-ebooks.com/library/Robert Dabney/RLD_Systematic Theology.pdf
I suspect that Calvin on John 3:16 meant very close to how R. L. Dabney explains this. Yet, since I know in Rom. 11:11, 12 the word "world" refers to Gentiles as well as Jews, and in this section of John 3, Jesus speaks to "a man of the Pharisees" and "a ruler of the Jews" in v1; then in 10 "a master in Israel". I understand Jesus to be emphatically letting this Jew know that God loves Gentiles as well as Jews.