I'll summarizes some of the main points of the video here.  This is largely a question of if the authority of Scriptures, the reliability of the translation of  Scripture, the infallibility of Scripture (as communicated by God the Holy Spirit to the original authors) and the clarity with which God communicated His message to His intended audience.  I typically follow the Historical-Grammatical approach to Biblical Interpretation (see How to Interpret the Bible which speaks of the various approaches to biblical hermeneutics).  With that in mind, a key verse here would be Exodus 20:11 (the justification for the fourth commandment), "For in six days the Lord made the heavens and the earth, the sea, and all that is in them, and rested on the seventh day. Therefore the Lord blessed the Sabbath day and made it holy."  This leaves no room for Progressive Evolution, The Gap Theory, or any other Theistic Evolution model that tries to insert millions, billions, or even trillions of years into the Bible (what some people call "deep time").

Without the creation account of Genesis 1, the story of Adam and Eve which gives the foundation of law, government, family, and the good work that God calls us to to "keep" (protect and cultivate) His creation don't make sense.  We then also can't explain the existence of sin and death which are explained by Genesis 3, and then the whole gospel falls apart because if there is no First Adam, there is no need for a Second Adam. 

Also, the end of Revelation doesn't make much sense without a literal interpretation of Genesis as the end is a better version of the beginning.  We see the Tree of Life as bookends of the story--Adam and Eve are kept from the Garden so that they might not eat of the Tree of Life after they sinned, but the Tree of Life is available for all to eat freely in the New Heavens and New Earth.  The video makes other good points, but these were a few that I wanted to highlight.

This article was originally written in response to a question posed by a student at the school I work for. The question was specifically about why it is fair that the world is being judged today for Adam's sin. I explained first that each of us as humans have free will and have used that free will to commit sin. If we look at ourselves honestly, all of us have chosen to rebel against God and we ourselves are responsible for those choices that we have made with the free will that has been given to us.
However, what Adam's sin did was that it changed our nature. Where Adam and Eve were created, they were made to be in perfect communion with God and loved being in His presence. When sin entered the world, they desired instead to rebel against God and do what they felt was right--trying to decide good and evil for themselves. Every generation since them has now been born with that same tendency to rebel against God and do what is contrary to His Law and divine nature. They neither desire to know Him nor worship Him, and they definitely don't desire to obey Him.
I asked the student if a child had to be taught to lie or taught to tell the truth? The student said that lying comes naturally. I then asked if lying was rebellion against God's Law (sin)? The student agreed it was. We talked about several other examples, but the point was made that the very first time that any of us (even a child) willfully sinned in any way that they knew was wrong, they now have their own sin that needs to be atoned for and we cannot blame that sin on Adam. It will be for our own choices and actions that each of whom choose to be judged by our own works will one day answer for when the books are opened. We will not answer for the sins of our ancestors, nor will we answer for the sins of our descendants. However, there is a choice—you do not have to be judged by your works. You can choose instead to be judged by the works of Jesus, and your name would be written in a different book—The Lamb’s Book of Life! Only those whose name is found in this book will be allowed entry into the New Heavens and the New Earth.

There is something to be said here for God visiting the sins of the fathers on the third and fourth generation because the consequences of sin are long-lasting and multi-generational. There is no such thing as a "personal choice" to sin that doesn't affect everyone else around you in some way. That's why I personally can't buy into the Libertarian philosophy that liberty should mean anarchy where there are no rules and everyone does whatever they want. God's rules are what is best for us personally, for our families and for our society and culture. It is because He loves us that He gives us good rules to follow. It is because we do not love Him that we break His rules and act as if we want to be our gods with a little 'g.'

So then what about the fact that Nature and all Creation was corrupted by sin? How is it fair that things that had no capacity to sin before are now broken and not like they were to start off? Are the plants and animals and ground all being judged because of Adam's original sin or our own? The answer is "Yes" to both. Everything in creation "fell" when Adam sinned because Adam was the federal head of creation. Romans 5 talks about this but everything that was "in Adam" (all of mankind and all of creation) fell when Adam sinned, but "in Christ" all of us can be made new. One day there will be a New Heaven and a New Earth that is no longer corrupted by sin. We will be restored to what it was like in the Garden of Eden only better. This time there will be not just one man and one woman, but men and women from every tribe, tongue, and nation of the earth. All people groups will be represented. We will no longer need to be sexual creatures because the need for reproduction won't exist--there will be no more death and no more aging. In fact, there won't even be any more time. We will no longer even have the sun or the moon to tell us whether it is day or night. We will just always be in the light of His presence forever and ever and it will always be eternal day. There will be no more need to sleep, but we will have good work to do just like Adam and Eve did when the LORD told them they were cultivate and protect the Garden that He entrusted to them.

One day, the righteous will be rewarded for the acts that were done to glorify Christ, but these rewards will ultimately be laid at the feet of Christ because He is the one who did the work in and through us and He deserves the glory, not us. These works come after salvation and are not the means of salvation (I do not work up enough righteousness for God to accept me). This is what separates Christianity from every other religion that I know of. “Judgment Day” is not where there is some kind of scale or balance to see if your “good” deeds outweigh your “bad,” for none of us have any chance in any kind of system like that. Instead, there is a registry of the two kingdoms—the kingdom of God, and the kingdom of this world. To which kingdom do you belong? You will not be allowed entry into the kingdom of God if you are not a citizen of His kingdom, and only Jesus has the authority to make you a kingdom citizen by choosing you to be adopted into His family (more on the idea of Adoption later).

The condemnation of Adam’s sin hangs over all creation, including all of us, and that is why we all need to be made new, and the kingdom of God is not a kingdom of this world (see Jesus’ conversation with Pilate in John 18:36). It is why we needed a Second and Final Adam to be the federal head of this new kingdom, and we needed a way to become citizens of this new kingdom that had nothing to do with our sufficiency or adequacy, because we have neither. When I stand before Christ one day, I will be judged on His sufficiency and adequacy, and not my own. That is the good news of the gospel, and it is the only answer to the issue of Original Sin.
There is therefore now no condemnation to those who are in Christ Jesus, who don’t walk according to the flesh, but according to the Spirit. (Romans 8:1)