There is a huge flaw in this particular message from John McArthur. He wrongly states that the people who believed in Christ were not saved. However, in both John 10, and in John 14, Jesus tells them to come to faith in God in the exact same way, because of the works He is doing; having faith which will get into the kingdom.
"Now when He was in Jerusalem at the Passover, during the feast, many believed in His name when they saw the signs which He did. But Jesus did not commit Himself to them, because He knew all men, and had no need that anyone should testify of man, for He knew what was in man." John 2:23-25.
"If I do not do the works of My Father, do not believe Me; but if I do, though you do not believe Me, believe the works, that you may know and believe that the Father is in Me, and I in Him." John 10:37-38
"Philip said to Him, �Lord, show us the Father, and it is sufficient for us.� Jesus said to him, �Have I been with you so long, and yet you have not known Me, Philip? He who has seen Me has seen the Father; so how can you say, �Show us the Father�? Do you not believe that I am in the Father, and the Father in Me? The words that I speak to you I do not speak on My own authority; but the Father who dwells in Me does the works. Believe Me that I am in the Father and the Father in Me, or else believe Me for the sake of the works themselves." John 14:8-11
Jesus urges belief in Him for the very same reason McArthur says they are not saved. Jesus says it brings them into a relationship with God. I choose Jesus' interpretation of the significance of "believ(ing) (Him) for the sake of the works themselves".
I should add that the John's statement regarding Christ's failure to entrust Himself to man is a foundational truth.
"But Jesus did not commit Himself to them, because He knew all men, and had no need that anyone should testify of man, for He knew what was in man."
Jesus never entrusted Himself to any man or to man as a group; but always entrusted Himself to the Father and the Holy Spirit. It is a truth that was not based on the level of faith, or lack thereof, of anyone else. This is an evidence of the unique nature of Christ, not evidence of lack of relationship with God on the part of those who believed upon Him that day.