"Spirit" indicates the vital principle of, the essential nature of, the heart and core of prophecy. In other words, the testimony of Jesus is the heart and core of prophecy. We should not define prophecy too narrowly, because prophecy means either "inspired speaking" (forth-telling) or "foretelling" (predicting). The testimony of Jesus Christ is the heart and core of inspired speaking and writing, as well as predictive speaking or writing.
Jesus' testimony consisted of two things: first, the example that He set in the way that He lived His life and what He did, as well as, second, the words that He spoke, His message. His message is the gospel - the good news of the Kingdom of God, of God's purpose, of why we were born, of Christ dying for our sins, of God reproducing Himself, of His creating us in His image and how He is doing it - and that news is spirit. It is life.
"The testimony of Jesus is the spirit. . . ." The gospel is the spirit, the heart and core, the essence, of the mind of God as it pertains to man. It contains many facets, but what He said is central to everything else in the Bible. Added to it is God's active participation in the actual creation of each potential God-being, watching over His family, molding and shaping His children into what He wants them to become.