If this were not the case, consider how a resurrection-denying Corinthian "believer" could've responded to Paul's rhetorical questions: "But Paul, isn't it your belief that people continue to live in a conscious, disembodied state after their body dies? Don't you believe that those who die in Christ are, right now, enjoying the Lord's presence in heaven? How then can you say that there is no benefit - that there is nothing to be gained - if you die? How can you say that the dead in Christ have perished?" Even if Paul himself didn't believe this but his view merely allowed for it, his argument would've been completely undermined.
If Christ has not been roused, then he's still just as dead as he was after he breathed his last on the cross. If Christ has not been roused, he would, today, be nothing more than the skeletal remains of a corpse. And if Christ himself was not delivered from death and restored to a living existence, then we have no reason to expect anything better. But - thank God! - "Christ has been roused from among the dead, the Firstfruit of those who are reposing" (1 Cor. 15:20). Our resurrection depends on Christ's, and Paul's statements in verses 29-32 imply that if the dead are not roused then not only would Christ not be roused but Paul would be left without any reason to live the way he did. After this life ended he would simply remain dead for all time.
In this clip, Laurie asserts that "A believer - that is, a follower of Jesus Christ - never dies." Most Christians, I think, actually believe this. When they think about their (Christian) loved ones who've died, they don't imagine them as lying lifeless in a grave, or as reduced to ashes in an urn. No; most likely, they imagine them as enjoying the bliss of heaven in the presence of Christ and God. I think that most Christians - if they were honest - would agree with Laurie. They just don't articulate what they really believe as boldly and as clearly as Laurie has done. Laurie goes on to support his bold assertion with the words of Christ in Mark 12:18-27. Laurie claims that, because God said "he IS the God of Abraham, Isaac and Jacob" (rather than he was their God), these three patriarchs "live in eternity." And he goes on to say that "your loved ones who died in the Lord - they still live. So a Christian never dies." Death, then, is not really an enemy (as Paul says). According to Laurie and most Christians (if they were honest), death - and being dead - is merely an illusion.
Even before the birth of the promised child Isaac, God told Abraham, "No longer shall your name be called Abram, but your name shall be Abraham, for I have made you the father of a multitude of nations" (Gen 17:5). Was Abraham "the father of a multitude of nations" at the time God spoke to Abraham? No; God was speaking in view of the fact that he was going to fulfill this promise made to Abraham, and that Abraham would, in fact, become the father of a multitude of nations.