I believe this refers to all human sin, or (to borrow from John Calvin) "all men indiscriminately". Christ being the Propitiation for all sins is not a problem for historic Calvinism (although I believe both historic and neo Calvinism to be incorrect). As many Greek scholars have pointed out, the subject of the passage is Christ and not man's sins.Here is an article for you to read. If you are going to maintain that whole world does not mean all people then it is you that has to provide the rational reasons from within the context as to why you think that way.
Let’s do this, let’s look at John’s use of “world” in 1 John to see how John would use the term. For this study, I will be using Dr. Robert Picirilli’s book, Grace, Faith, FreeWill. The Greek word is “kosmos” G2889 and it occurs 23 times in 1 John. Dr. Robert Picirilli notes the use of kosmos in 1 John as follows:
1Jn_2:2
1Jn_2:15-17 (6 times)
1Jn_3:1
1Jn_3:13
1Jn_3:17
1Jn_4:1-5 (6 times)
1Jn_4:9
1Jn_4:14
1Jn_4:17
1Jn_5:4-5 (3 times)
1Jn_5:19
Picirilli notes that the use of “the world” can be used personally by John (1Jn_3:1, 1Jn_3:13) or impersonally (1Jn_2:15). The use of “world” in 1Jn_2:2 is personal.
John consistently uses “the world” against the Church. Only four times in 1 John does he use “the world” to not be negative: 1Jn_3:17 and 1Jn_4:17; 1Jn_4:9; and 1Jn_4:14 which is the same meaning as in 1Jn_2:2. The Church is not to love “the world” (1Jn_2:15-17), does not recognize Jesus nor His disciples (1Jn_3:1), hates disciples (1Jn_3:13), has the spirit of the antichrist (1Jn_4:3-4), is overcome by disciples (1Jn_5:4-5), and is in the grip of the evil one (1Jn_5:18-19).
What does John mean by “world”? He uses this word 23 times in this short letter, consistently indicating the very opposite of the people of God. The people of God and “the world” are two different peoples, hostile to each other. Surely John uses “world” in 1Jn_2:2 in the same way, and not as a reference to the rest of the elect in the world.
All of us who handle God's Word do well to remember that we do not honor Him with our interpretive ingenuity but with submission to what He says. To say, even to show, that a given statement can be interpreted in a certain way does us no credit at all. The question is always not what the words can mean but what they do mean, here. In 1Jn_2:2 and in 1Ti_2:1-6, the most obvious meaning of "world" and "all men" is universalistic. In these cases, careful exegesis supports the obvious meaning. Dr. Picirilli
Making it appear that this would be a double payment is, obviously, a fallacy because it assumes Calvinism is correct (it is from a distinctively Calvinistic point of view).