The first question one must ask is, “In this context, just what is it that John believed?” John certainly must now have believed Mary’s report, that the body of Jesus was missing. I think he believed more than this. I think he believed that Jesus had somehow been raised from the dead, though he did not yet understand how or why. The point here seems to be that John believed in the resurrection of our Lord before he even knew or realized that he was supposed to.
Throughout the Gospel of John, the word “believe” is employed in various ways, and the content of what is believed is not always the same. The situation at this point in time (during our Lord’s earthly life and ministry) was unique. The Messiah had come, but He had not yet died, been buried, resurrected, and ascended into heaven. From John chapter 1 we see the disciples believing (that Jesus was the Messiah—something they did not yet understand the meaning of. Their belief grew throughout the life and ministry of Jesus. Who can say at what moment the disciples really were saved?
I think you could say that the “belief” of everyone, prior to our Lord’s resurrection and ascension, was less than full-fledged, because they did not have all the facts. In the context, we must ask just what it was that John believed.
I do think that believing in the resurrection of our Lord is a vital part of the Gospel, which we must believe (Romans 10:9), but once again, this is after He has been raised, and the meaning of His resurrection has been made clear.