Be that as it may, the grammar is parallel between the two verses, and the verb in verse 15 points back to the pronoun in verse 14:
{heis huper pantôn apethanen} one over all he-away-died
{huper pantôn apethanen} over all he-away-died
The “he” in “he died” is implied by the verb form in both verses. In verse 14 there is also a pronoun for the verb, “one” (masculine to match the verb), but since neither verb actually requires a noun or pronoun, unless there are clear reasons to think otherwise the parallel phraseology would connect verse 15’s clause back to the subject of the prior clause, the “one” who from-died over all.
But none of that really matters: unless we are supposed to be putting our faith in Adam for eternal life, verse 15 is about Christ (as no one I’ve ever read or heard of disputes), and verse 15 is thus clear that Christ died away (i.e. into hades) and was raised over all.
Thus, even if we interpret {huper} (i.e. “hyper”) as meaning “over” instead of “for the sake of” (which is possible), we have the following statement regardless of verse 14 (which changes nothing in this regard):
“He died-away over all so-that the living-ones should by no means still be living to themselves but to the one dying-away and being raised over them.”
This does allow a Calvinist or Arminian interpretation (as well as universalist), however, if {huper} is interpreted as an authority reference (“over X”) rather than an intentional reference (“for the sake of X”), the latter of which I doubt a Calvinist could accept: all three Christian soteriologies agree (at least nominally) that Christ dies and lives in authority over all, and that all have died, and that Christ’s goal was so that those who have died whom He makes live (in whatever sense that may mean) will no longer live for themselves but for the One who died and lived for them.
If “for sake of” is acknowledged to be the proper interpretation (although I don’t know any immediate grounds for saying so, but neither for it only meaning an authoritative “over” either), the verse probably couldn’t fit Calv soteriology, but it might still fit Arm: there is nothing here speaking of the certainty of Christ’s success in bringing those He chooses to live back to loyalty to Himself rather than continuing rebellion. I don’t see anything in the nearby context to point that way either.
(Obviously I find plenty of places elsewhere pointing to that, just not nearby here. The nearby subsequent verses 18-21 about God reconciling the world to Himself wouldn’t fit Calv soteriology, and might be grounds for interpreting {huper} earlier to mean “for the sake of” without losing the authority implied; but again there is nothing there about the certainty of Christ accomplishing this reconciliation. On the contrary, Paul goes on to warn the Corinthians in the next verse 6:1, not to receive the grace of Christ for nothing! Then again, to believe that some may finally receive the grace of Christ for nothing, or that the grace of Christ may not accomplish reconciliation sooner or later “for the world”, might be tantamount to regarding if not receiving the grace of Christ as being vain!–which we have certainly been warned about doing elsewhere! 
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