The four eschatological viewpoints described are quite different and to a large extent mutually exclusive. Furthermore each viewpoint has adherents with different concepts of what that viewpoint actually describes, so it hard to be too definitive. Some history of the passage would help put them in perspective.
It is generally accepted that Isaiah chapters 1-39 were written by Isaiah, son of Amoz, who lived during the reigns of Kings Uzziah, Jotham, Ahaz and Hezekiah of Judah, although there were numerous later additions and changes to that portion of the book. Chapters 40-55 are attributed to an anonymous author now known as Second Isaiah or Deutero-Isaiah, who lived during the Babylonian Exile. This author had a very different style to that of First Isaiah, who used brief, emphatic diction, compared to Second Isaiah's poetic style and more extensive vocabulary. Chapters 56-66 are attributed to another anonymous author now known as Third Isaiah or Trito-Isaiah, who lived shortly after the Return from Exile. So, chapter 65 can be seen as referring to the hopes and aspirations of the Jews who had recently returned from Babylon. We can see the hardships of captivity compared to the joys of freedom:
- There shall be no more thence an infant of days, nor an old man that hath not filled his days: for the child shall die an hundred
years old; but the sinner being an hundred years old shall be accursed
- And they shall build houses, and inhabit them; and they shall plant vineyards, and eat the fruit of them. They shall not build, and
another inhabit; they shall not plant, and another eat ... (Isaiah
To Third Isaiah, freedom was such a wonderful experience that he compared it to paradise, as in verse 65:25:
The wolf and the lamb shall feed together, and the lion shall eat straw like the bullock: and dust shall be the serpent's meat. They shall not hurt nor destroy in all my holy mountain, saith the LORD.
Premillennialism is the belief that Jesus will literally and physically return to earth before Christ's reign for 1,000 years during a golden age of peace. However, there are two very distinct schools of premillennialism, historic premillennialism and dispensational premillennialism, which is largely based on the nineteenth-century ideas of Darby and Schofield. Premillennialism is largely based on interpretations of the Books of Daniel and Revelation, along with the the Olivet discourse from the synoptic gospels, but Isaiah 65:17-25 fits in well with this view. Wayne Jackson, in an article entitled 'Examining Premillennialism' draws on Isaiah to support the concept of premillennialism, but does not mention verses 65:17-25.
Postmillennialism expects that eventually the vast majority of those living will be saved. Increasing gospel success will gradually produce a time in history prior to Christ's return in which faith, righteousness, peace, and prosperity will prevail in the affairs of men and of nations. Postmillennialism also teaches that the forces of Satan will gradually be defeated by the expansion of the Kingdom of God throughout history up until the second coming of Christ. Many postmillennialists also adopt some form of preterism, which holds that many of the end times prophecies in the Bible have already been fulfilled. Although I see Isaiah 65:17-25 as less of a good fit here, because the the age that began in the first century and will continue until his final coming has not so far been like a paradise on earth, some postmillennialists see it as being at least a figurative reference to postmillennialism.
Full preterism says that the destruction of Jerusalem fulfilled all eschatological or 'end times' events, including the resurrection of the dead and Jesus' Second Coming, or Parousia, and the Final Judgement. Partial preterism holds that most eschatological prophecies, such as the destruction of Jerusalem, the Antichrists, the Great Tribulation, and the advent of the Day of the Lord as a "judgement-coming" of Christ, were fulfilled either in 70 CE or during the persecution of Christians under the Emperor Nero, but that the second coming and the resurrection of the dead have not yet occurred. Preterism does not focus on an earthly paradise like that portrayed in Isaiah 65, although like all Christian eschatology it looks forward to eternal paradise after the final judgement. Nevertheless, some preterists do see echoes of preterism in Isaiah 65:17-25.
The question asks what other views there are. One view that has to be discussed is that the passage can only be read literally, reading verses 65:17-25 as the author originally intended them to be read. On this view, it is simply a statement of hope for the new Jerusalem and the new land the Jews were to begin building after the Return from the Babylonian Exile, with God's help.