The luminous mysteries show Jesus’ light in the world. Jesus is fully human and fully divine, and the mysteries we contemplate seem to give full recognition to each, through stories of Jesus living out his public ministry.
The fruits of each glorious mystery are listed as follows: faith, hope, wisdom, devotion to Mary and the grace of a happy death. Slowly but surely, I could see them playing out in my own life.
As the first superior general of the Society of Jesus, St. Ignatius wrote a book in which he described the Society’s mission, internal structures and way of proceeding.
I suspect that there are other Catholics who may pray it in their own way, too. And, to my mind, any way you pray that leads you closer to God makes sense.