Just like Loftus, this man can't tell a difference between "being" and "person". This is a category error. "Being" and "person" are not the same thing at all. Christians do not believe that God is three person in one person or three beings in one being. God is three persons in one being. If you make the correct distinction between "being" and "person" there is no need for confusion. A human being is one person. Who say that God, who is infinite and so different from us on any measurable level, why would we think God is limited just as us.
Another example of where the video fails is the "Logos" discussion. The mistake is thinking that Jesus had a beginning. He didn't. The Logos is eternal.
In the beginning was the Word, and the Word was with God, and the Word was God. 2 He was with God in the beginning. 3 Through him all things were made; without him nothing was made that has been made. - John 1:1-3
Well at least the man recognized that Jesus is the Logos.
Debunking Christianity: Rhetorical Bullshit: The John Loftus Trinity Argument