In the same way, to say "On this Ecumenical Sunday, let us pray for those of other denominations and those of other faiths" is wrongheaded. We should indeed pray for those of other faiths (especially that they would come to know the saving love of God in the Lord Jesus Christ!), but that has nothing to do with ecumenism.
The word "ecumenical," from the Greek oikoumene which means house/household, means "all who belong to the household of the Father." To be sure, all people were created and are loved by God. But the notion of belonging to the household of the Father without reference to Jesus Christ is a nonstarter:
"I am the way and the truth and the life. No one comes to the Father except through me." (John 14:6)In other words, for us sinful human beings, who ran away from home and cut off all ties with the Father, NOT to travel the "road home" of believing in Jesus and being bound to him, and still to say that person belongs to the household of God is not only nonsense, but an affront to the free will and dignity of non-Christians.
"The Spirit you received does not make you slaves, so that you live in fear again; rather, the Spirit you received brought about your adoption to sonship. And by him we cry, 'Abba, Father.'” (Romans 8:15)
We should pray for our brothers and sisters in Christ, and we should pray for those who do not know Christ and are not united to Him.
But to try and force the two into the word "ecumenical" not only renders null and void the incarnation, death, and resurrection of Jesus Christ, but is a simple abuse of language.