"And there is none from the people of the book except that he surely believe in it before his death."
It - the aforementioned event of crucifixion.
His - the Jew/Christian/people of the book
So let's translate it as the following:
"And there is none from the people of the book except that he will surely believe in [Jesus's death on the cross] before his [person of the book's] death."
This makes the most sense. In order for a Jew to remain a Jew, he must believe that Jesus (as) died a cursed death on the cross since it shows he was not a true prophet (See Deuteronomy 21:22-23).
And in order for a Christian to remain a Christian, he must also believe that Jesus (as) died a cursed death on the cross since it is the entire basis for their dogma of atonement. And it is a must for every Jew/Christian to keep this belief until their death.
So, by negating the idea that Jesus (as) died on the cross, the Quran beautifully counters this belief by both the Jews and the Christians by establishing Jesus's (as) prophethood and destroying the concept of atonement.
The often-mentioned idea that all Jews/Christians will believe in Jesus (as) before Jesus's (as) death is not in accordance with the Quran or logic. First of all, the Quran makes it clear that Jews and Christians will remain until the Day of Judgement:
"And from those also who say, ‘We are Christians,’ We took a covenant, but they too have forgotten a good part of that with which they were exhorted. So We have caused enmity and hatred among them till the Day of Resurrection. And Allah will soon let them know what they have been doing." (5:14)
"And the Jews say, ‘The hand of Allah is tied up.’ Their own hands shall be tied up and they shall be cursed for what they say.... And We have cast among them enmity and hatred till the Day of Resurrection..." (5:64)
"When Allah said, ‘O Jesus, I will cause thee to die [a natural death] and will exalt thee to Myself, and will clear thee from the charges of those who disbelieve, and will place those who follow thee above those who disbelieve, until the Day of Resurrection..." (3:55).
If Jews and Christians are all supposed to become Muslims, then these verses will be meaningless. Yes, Islam is to be supreme above all other religions. But for these verses to remain true a small group of Jews and Christians would have to remain until the Day of Judgement, no matter how small or insignificant they may be.
Secondly, what about all the Jews since Jesus (as) that have passed away? They didn't believe in Jesus (as) and died while rejecting him. The claim that this verse refers specifically to the Jews/Christians during his second coming is illegitimate since nothing in these verses refer even remotely to a second coming.