I think the transision can happen both peacefully and unpeacefully. Let me assure there is not going to be any Hindu army which is going to form and then attack every nation on earth and convert them to Hinduism. Hindusim has never spread by the sword, wherver it has spread it has spread through peaceful acceptance. Again, 20 million Americans have not been forced to do Yoga. I am making no effort to convert anybody either, in fact if I was, I would be going the wrong way about doing it.
The ideal way it happens is that gradually the world becomes more and more Hindu and the Abrahamic religions accept it and accomodate it. For example, Christians can accomodate by emphasisng Christian gnostic teachings. Muslims can accomodate by looking towards Sufism, and Jews can accomodate by looking at Kabbalah. In this way we can have a global spirituality which everybody can practice. This can happen peacefully and naturally over time. It will happen because science itself will validate spirituality.
The non-ideal way it is going to happen is after the world experiences extreme suffering for the beliefs it does have today. The kind of way of life we have today, largely based on Abrahamic philosophy will lead to an unsustainable future for the planet and struggle for basic things like food and water. This will lead to massive conflict and war, possibly even world wars using WMD and billions could perish. The shock that humanity will receive from this will force it to adopting Hindu ways.
Either way Hinduism will take over at some point during this century. It is inevitable because the Satyuga will return and the authentic knowledge will once again prevail.