big denial from the Vatican is to say that the Holy Father did not carry out an exorcism. More or less every major news outlet seems to be carrying the story of the non-exorcism: after all, exorcism, even if it didn't happen, is a subject which is exciting for many people.
The Vatican news site continues with a short interview with Fr. Bernd Hagenkord, SJ which is very sensible. As a teacher of sacramental theology, I include an excursus on exorcism in my course. Fr Hagenkord rightly and briefly states that exorcism is not a sacrament. An interesting point for theologians is the question of whether exorcism is a sacramental. It is usually listed as such in the manuals, including that of the most excellent Felix Cappello. However, the highly respected theologian, Dr Manfred Hauke wrote in the periodical Antiphon (Vol 10. 2006) arguing that it was a specific priestly power given by Christ, not simply a sacramental instituted by the Church. I am sure he is correct in this.
Quite rightly the Church tries to avoid sensationalism on this subject. In fact, the devil's work is not an exciting horror-movie spectacular, it is sick, nasty, destructive, (and often revoltingly petty.) I think that the adversary's work is often accomplished most effectively in causing discord, jealousy, and hatred between good people. You don't have to be a tree-hugging hippy to draw the lesson from St John that the remedy is that we should love one another. This includes forbearance when we are wronged, patience with those who annoy us, and the spiritual scud missile of conscious acts of supernatural charity (however small and hidden) carried out with the motive of the love of God. Prayer to Our Lady, to the holy angels, the use of holy water and so on are all vitally important, but active charity is what really gets the tracks moving.
The video of Pope Francis praying over the disabled man does unfortunately give people a bit of spectacle (the disabled man's own physical reaction makes wild speculation possible but it may perfectly well be a purely natural reaction to the event of the Holy Father's attention.) To me Pope Francis' action looks very like the sort of prayer that happens at charismatic healing services - not surprising given the Holy Father's charismatic background. It might therefore be a prayer for deliverance if not strictly a simple exorcism (it is not a solemn exorcism because for that, the Pope would have the liturgical book to hand, put on a stole and read the prescribed prayers.)
I wrote a while back about Fr Jeremy Davies' good pamphlet on exorcism published by the CTS. It is worth remembering that any priest may carry out a minor exorcism if he prudently deems it appropriate. It is always important for him is to rely entirely on the power of Christ and to be ruthless in excluding any pride - especially the slightest thought that the good achieved might be anything to do with his own personal qualities.