Let it be said that the arguments given by Mr. Anderson overall lack consistency and require that one abandons common sense. The final standard by which all translations of the Bible should be evaluated is the oldest and best manuscripts available. We do not have the original autographs, and the Bible was not originally written in English.
The speaker in the video is an obvious anti-intellectual. Mr. Anderson does nothing whatsoever to negate the validity of claim that King James onlyism is circular reasoning. Instead, he makes a fool of himself in condemning Christians by using an extra-biblical standard (King James onlyism). Steven Anderson has embraced a theological contradiction because he also professes to believe in the formal sufficiency of Scripture.
Faith in the God of the Bible is not based on circular reasoning, as the speaker in the video asserts. In other words, there are multiple lines of evidence to support the veracity of Christian claims. There are various philosophical arguments for the existence of God. There is fulfilled prophecy. There is consistency with world history and numerous archaeological discoveries. There is a wealth of manuscript evidence for the New Testament (what some have termed "an embarrassment of riches").
Jesus Christ and the twelve apostles performed miracles in order to validate their ministry, which was in accordance with Scripture. He even stumped His critics in posing difficult questions. The Apostle Paul said that God's existence is confirmed by observing nature (Romans 1:20). Consequently, we clearly see that biblical Christianity has never advocated for blind faith.
Most of the heresies that we witness today originated in the early church. There are different variations of false teachings from the early days of Christianity in our modern age which long predate the production of the King James Version. A notorious example would be Arianism and the Watchtower Society. So, the issue is not translations such as the New American Standard Bible or the English Standard Version (as Steven Anderson and the likes of him ignorantly assert). The real issue is that people abuse Scripture to fit their preconceived ideas.
The 1984 publication of the New International Version is sound. Later editions of that translation have the problem of gender-inclusive language. Anyway, see this article for more information on the King James Only Movement:
If one has a preference for the King James Version, then that is perfectly acceptable. Stick with it.
Finally, it should be pointed out that "Pastor" Steven Anderson is a false teacher. He opposes the necessity of repentance, Christ's Lordship, and believes that homosexuals (along with others) should be put to death. He claimed in a sermon that the Bible is God Himself. Steven Anderson has vitriolic sermons that are simply hate speech, which is a sign of not being led by the Holy Spirit (Galatians 5:22-23). This pastor does not have any grace and compassion for sinners. He is a self-righteous Pharisee. People like Steven Anderson claim to have been saved by grace, yet by their hatred show us they do not even understand what that term means.
If we all at this very moment consistently subjected ourselves to the Law, then we would all be dead because we have all sinned against a holy God. His moral standard is that of perfection. Nonetheless, the biblical gospel is a call to spiritual conversion (Luke 13:1-3). Steven Anderson also believes that Jesus Christ was punished in hell for three days. So this man is definitely one that we should avoid!
ADDENDUM: One reader pointed out a well-done analysis of Steven Anderson's gospel teaching by Mike Winger which can be found here.