Did the Christian bible corrupt Isaiah verse 8:23

I did not watch the entirety of Rabbi Singer's video, so my answer here is based largely on the information provided in the OP, which asks the question, "Did the Christian bible [sic] corrupt Isaiah 8:23".

Counterpoint 1: The NIV is not the "Christian bible"

The NIV may or may not represent what most Christians accept as having valid translations of the verses in Isaiah and Matthew, but the OP presumes that this is the case.

If one were to look at the huge variety of Christian Bibles, one would find many different ways that this passage is translated, largely depending to the extent that the version relies on the Masoretic Text, the Latin Vulgate, the Greek Septuagint, or some other proto-text (e.g. the Peshitta).

Counterpoint 2: Rabbi Singer's translation of the Old Testament text is not necessarily correct

The OP quotes Isaiah 8:23-9:1 as:

8:23 For there is no weariness to the one who oppresses her; like the first time, he dealt mildly, [exiling only] the land of Zebulun and the land of Naftali, and the last one he dealt harshly, the way of the sea, and the other side of the Jordan, the attraction of the nations.

9:1 The people who walked in darkness, have seen a great light; those who dwell in the land of the shadow of death, light shone upon them.

Another Jewish translation of this text - from the 1985 Jewish Publication Society Tanakh reads:

8:23 For if there were to be any break of day for that which is in straits, only the former would have brought abas*m*nt to the land of Zebulun and the land of Naphtali—while the later one would have brought honor to the Way of the Sea, the other side of the Jordan, and Galilee of the Nations.

9:1 The people that walked in darkness Have seen a brilliant light; On those who dwelt in a land of gloom Light has dawned.

A third Jewish translation is available, but it is only available in Greek and dates from the 2nd century BC (from the Septuagint). It reads, in English translation (Brenton):

9:1 Drink this first. Act quickly, O land of Zabulon, land of Nephthalim, and the rest inhabiting the sea-coast, and the land beyond Jordan, Galilee of the Gentiles.

9:2 O people walking in darkness, behold a great light: ye that dwell in the region and shadow of death, a light shall shine upon you.

Yet another Jewish translation is found in the Oxford Jewish Study Bible - a slight variation from the JPS Tanakh version of verse 8:23:

8:23 For if there were to be any break of day for that [land] which is in straits, only the former [king] would have brought abas*m*nt to the land of Zebulun and the land of Naphtali—while the later one would have brought honor to the Way of the Sea, the other side of the Jordan, and Galilee of the Nations.

These are radically different interpretations of the same verses, all by Jewish sources (we can overlook the difference in verse numbering, which is irrelevant and does not arise from the underlying texts themselves).

As (Jewish) Professor Benjamin Sommer, Professor of Bible and Ancient Semitic Languages at the Jewish Theological Seminary, explains in his commentary, the meaning of the Masoretic Text of these verses is actually uncertain. The explanation given for the Jewish Study Bible Reading rendering is:

Meaining of verse uncertain. The rendering here assumes that "the former [king]" refers to Pekah (cf. 2 Kings 15:29) and "the later" to Hosea (ibid. 30). For the construction lu ... ka'eth, see Judg. 13-23.

Thus, without looking too deeply, we have four different interpretations of Isaiah from three different Jewish sources that span two millennia. (viz. Two Jews, Three Opinions).

If, as at least some Jewish scholars seem to believe, that the Masoretic Text of Isaiah is, in fact, uncertain, and Rabbi Singer is himself consulting the Masoretic Text, it is hard to find the logic in arguing that one translation of an uncertain text does not agree with another translation of the same uncertain text.

Counterpoint 3: The allusion found in the New Testament is not corrupt

Rabbi Singer seems to be trying to call attention away from Christ's quotation of Isaiah 9:1/2 and focusing on Christian translations of the Old Testament text itself (which not even Jews can agree on). In fact, as the OP example shows, Matthew 4:16 agrees almost perfectly with the "Jewish" text that Rabbi Singer quotes. In fact, if we look at the Greek, there is almost literal agreement with the Septuagint - which is a Jewish text:

LXX

ὁ λαὸς ὁ πορευόμενος ἐν σκότει ἴδετε φῶς μέγα οἱ κατοικοῦντες ἐν χώρᾳ καὶ σκιᾷ θανάτου φῶς λάμψει ἐφʼ ὑμᾶς

Nestle-Aland, 27th ed.

ὁ λαὸς ὁ καθήμενος ἐν σκότει φῶς εἶδεν μέγα καὶ τοῖς καθημένοις ἐν χώρᾳ καὶ σκιᾷ θανάτου φῶς ἀνέτειλεν αὐτοῖς