Calvinists see the "whole world" in this passage as referring to the elect throughout the world, particularly emphasizing that Christ died for Gentiles as well as Jews.
Examples of this approach abound. John Gill:
that is, not for the Jews only, for John was a Jew, and so were those he wrote unto, but for the Gentiles also (source)
Similarly, Matthew Poole writes:
i.e. for all that truly believe in him, all the world over. (source)
John MacArthur more thoroughly explains his view of John's intention here:
In the Jewish context, they understood Day of Atonement, they understood the language of propitiation. John is telling them that the sacrifice that Jesus offered is not just for the nation Israel, it's now for the world because the Lord is calling out a people for His name from every tribe and tongue and people and nation. (source; emphasis added)
Many other Reformed theologians take similar approaches, including John Frame (Systematic Theology, 907), the Reformed Study Bible, Louis Berkhof (3.3.6.B.4.a), and John Piper (source).
We can dive a bit deeper into the analysis of one Reformed theologian to get a better understanding of the rationale for this view. Simon Kistemaker (Exposition, 253–255), referring to the oft-cited "sufficient for the whole world but efficient for the elect" language, agrees with Calvin that while this is true, it is not in view here (see Calvin's commentary). He argues:
The phrase the whole world relates not to every creature God has made, for then the fallen angels also would share in Christ's redemption. The word whole describes the world in its totality, not necessarily in its individuality.
In defense of this idea, Kistemaker points to 1 John 3:16, where he sees John, after making a distinction between the "children of God" and the "children of the devil," saying that "Jesus Christ laid down his life for us" (emphasis added). He also argues, citing A. T. Robertson, that a different Greek word could have been used if John meant to say that Christ died for every individual:
John chooses the adjective ολος (whole) instead of πας (every, all) to communicate the idea of universality. The word ολος has "an indefinite meaning which πας does not have."