I meant the purpose of a prayer for others (in the Catholic sense) is a request to God. I pray that my brother is granted X I pray that my children remain safe, etc.

What you describe there in that we should love all equally is Christian thinking as per the Gospel, which I agree has many similarities with that Budhist meditation exercise but is not specific to a prayer for other people.

But you must act on this love, and there are many ways, through our daily actions, but also through prayer. I think it should come quite natural to any devout Christian.

My whole point is that I find it interesting, and surprising, how western psychologists are taking concepts from eastern religion, completely ignoring the western religious tradition.

Often they're "completely ignoring" the Eastern tradition as well. Meditation in a strict sense is not even that widespread in Eastern practice; it's generally practiced by monks, or perhaps by laity on a rare, focused spiritual retreat - so quite similar to mystical contemplative prayer in the West.

OK! I guess this is also true!