Yes, Yeshua is the living Word... he is the Torah with flesh on it.
As John tells us,
John 1:1 ESV
(1) In the beginning was the Word, and the Word was with God, and the Word was God.
... as this passage unfolds John leaves no doubt of whom he is speaking,
John 1:14 ESV
(14) And the Word became flesh and dwelt among us, and we have seen his glory, glory as of the only Son from the Father, full of grace and truth.
As you have said 'written Word'... and what 'written Word' would that be? What written Word existed at the time of Jesus/Yeshua's birth? See... and we know that Jesus never changes, right?
Hebrews 13:8 ESV
(8) Jesus Christ is the same yesterday and today and forever.
The Word from cover to cover... that is Genesis through Revelation is the revealing of Jesus Christ... the entire book is of him.
Psalms 40:7 ESV
(7) Then I said, “Behold, I have come; in the scroll of the book it is written of me:
Quoted again in Hebrews confirming the context of Jesus:
Hebrews 10:7 ESV
(7) Then I said, ‘Behold, I have come to do your will, O God, as it is written of me in the scroll of the book.’”